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Social interaction allows to support the disease management by creating online spaces where patients can interact with clinicians, and share experiences with other patients. Therefore, promoting targeed communication in online social spaces is a mean to group patients around shared goals, offer emotional support, and finally engage patients in their healthcare decision-making process. In this paper, we approach the argument from a theoretical perspective: we design an optimization problem aimed to encourage the creation of (induced) sub-networks of patients which, being recently diagnosed, wish to deepen the knowledge about their medical treatment with some other similar profiled patients, which have already been followed up by specific (even alternative) care centers. In particular, due to the computational hardness of the proposed problem, we provide approximated solutions based on distributed heuristics (i.e., Genetic Algorithms). Results are given for simulated data using Erd ̈os-R ́enyi random graphs.

A central problem in graph mining is finding dense subgraphs, with several applications in different fields, a notable example being identifying communities. While a lot of effort has been put on the problem of finding a single dense subgraph, only recently the focus has been shifted to the problem of finding a set of densest subgraphs. Some approaches aim at finding disjoint subgraphs, while in many real-world networks communities are often overlapping. An approach introduced to find possible overlapping subgraphs is the Top-k Overlapping Densest Subgraphs problem. For a given integer k >= 1, the goal of this problem is to find a set of k densest subgraphs that may share some vertices. The objective function to be maximized takes into account both the density of the subgraphs and the distance between subgraphs in the solution. The Top-k Overlapping Densest Subgraphs problem has been shown to admit a 1/10-factor approximation algorithm. Furthermore, the computational complexity of the problem has been left open. In this paper, we present contributions concerning the approximability and the computational complexity of the problem. For the approximability, we present approximation algorithms that improves the approximation factor to 1/2 , when k is bounded by the vertex set, and to 2/3 when k is a constant. For the computational complexity, we show that the problem is NP-hard even when k = 3.

Social media can directly support disease management by creating online spaces where patients can interact with clinicians, and share experiences with other patients. Nevertheless, much more work remains to be carried out for providing and sharing an optimized information content. In this paper we formulate, from a theoretical perspective, an optimization problem aimed to encourage the creation of a sub-network of patients which, being recently diagnosed, wish to deepen their knowledge about their pathologies with some other patients, whose clinical profile turn to be similar, and have already been followed up within specific, even alternative, care centers. We will focus on the hardness of the proposed problem and provide a Genetic Algorithm (GAbased) approach to seek faster approximated solutions.

Castelli, M., Dondi, R., Mauri, G., & Zoppis, I. (2017). The longest filled common subsequence problem. In 28th Annual Symposium on Combinatorial Pattern Matching, CPM 2017 (Vol. 78). [14] Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.CPM.2017.14 Inspired by a recent approach for genome reconstruction from incomplete data, we consider a variant of the longest common subsequence problem for the comparison of two sequences, one of which is incomplete, i.e. it has some missing elements. The new combinatorial problem, called Longest Filled Common Subsequence, given two sequences A and B, and a multiset M of symbols missing in B, asks for a sequence B∗ obtained by inserting the symbols of M into B so that B∗ induces a common subsequence with A of maximum length. First, we investigate the computational and approximation complexity of the problem and we show that it is NP-hard and APX-hard when A contains at most two occurrences of each symbol. Then, we give a 3/5-approximation algorithm for the problem. Finally, we present a fixed-parameter algorithm, when the problem is parameterized by the number of symbols inserted in B that "match" symbols of A. publishersversion published

The concept of Architectural Barrier can be extended to the Web, in the sense that people with disability can experience problems in accessing pages which are designed for the able-bodied. Despite of this, many users with different kind of disabilities regularly access the web using some kind of Assistive Technology. This means they can use a variety of resources and web 2.0 tools, but they need to be on their own computers, with their own accessibility software and configuration, in order to use them at best. The Farfalla project is a web application which aims to allow users to set their accessibility preferences on a centralized website and then to apply them to every other website they will visit. This approach can work from any web browser, on (almost) any machine, even without administrative privileges: the only requirement is a javascript-enabled browser with internet connection. In order to accomplish this, the Farfalla script only needs to be included in a target web page in the form of a small piece of HTML code. The attempt is to move the accessibility solutions from the user’s computer to the web itself; in this paper is explained why, if widespread, this practice could be the base for a truly inclusive web

The Consensus Clustering problem has been introduced as an effective way to analyze the results of different microarray experiments. The problem consists of looking for a partition that best summarizes a set of input partitions (each corresponding to a different microarray experiment) under a simple and intuitive cost function. The problem admits polynomial time algorithms on two input partitions, but is APX-hard on three input partitions. We investigate the restriction of Consensus Clustering when the output partition is required to contain at most k sets, giving a polynomial time approximation scheme (PTAS) while proving the NP-hardness of this restriction.

The aim of this paper is to illustrate the approach and the solutions that have been adopted by the MILK system to deliver a knowledge management environment to support workers during their every-day activities. The main goal of MILK is to collect and organize the knowledge associated with documents and projects within an organization. Profiling through metadata is the approach to classify, organize, retrieve and present knowledge. People are also profiled and organized in project teams and communities of interest to capture user needs and let the system supply users with comprehensive access to knowledge.

In this paper we review some of the existing projects available in the bioinformatics field for facilitating the development of programs, but for which minimising the running time is not of primary importance. We point out the advantages of open source libraries for such tasks and we discuss some of the open source licenses available. Finally, we present the project ALiBio, which is aimed at facilitating the development of efficient programs in bioinformatics.

The problem of matching a query string to a directed graph, whose vertices are labeled by strings, has application in different fields. In this paper we present results on the complexity of the approximate matching problem, where edit operations are symbol substitutions and are allowed only to the graph labels or both to the graph labels and the query string. We show that deciding if there exists a path in a graph that represents a query string with edit operations to vertex labels is an NP-complete problem and it is fixed-parameter tractable when parameterized by the length of the input string. We show that the variants of approximate string matching we consider are not fixed-parameter tractable, when the parameter is (1) the length of the query string and (2) the number of edit operations. Moreover, we provide inapproximability results for these variants of the of approximate string matching problem.

The Burrows-Wheeler-Transform (BWT), a reversible string transformation, is one of the fundamental components of many current data structures in string processing. It is central in data compression, as well as in efficient query algorithms for sequence data, such as webpages, genomic and other biological sequences, or indeed any textual data. The BWT lends itself well to compression because its number of equal-letter-runs (usually referred to as $r$) is often considerably lower than that of the original string; in particular, it is well suited for strings with many repeated factors. In fact, much attention has been paid to the $r$ parameter as measure of repetitiveness, especially to evaluate the performance in terms of both space and time of compressed indexing data structures. In this paper, we investigate $\rho(v)$, the ratio of $r$ and of the number of runs of the BWT of the reverse of $v$. Kempa and Kociumaka [FOCS 2020] gave the first non-trivial upper bound as $\rho(v) = O(\log^2(n))$, for any string $v$ of length $n$. However, nothing is known about the tightness of this upper bound. We present infinite families of binary strings for which $\rho(v) = \Theta(\log n)$ holds, thus giving the first non-trivial lower bound on $\rho(n)$, the maximum over all strings of length $n$. Our results suggest that $r$ is not an ideal measure of the repetitiveness of the string, since the number of repeated factors is invariant between the string and its reverse. We believe that there is a more intricate relationship between the number of runs of the BWT and the string's combinatorial properties., Comment: 14 pages, 2 figues

The problem of matching a query string to a directed graph, whose vertices are labeled by strings, has application in different fields, from data mining to computational biology. Several variants of the problem have been considered, depending on the fact that the match is exact or approximate and, in this latter case, which edit operations are considered and where are allowed. In this paper we present results on the complexity of the approximate matching problem, where edit operations are symbol substitutions and are allowed only on the graph labels or both on the graph labels and the query string. We introduce a variant of the problem that asks whether there exists a path in a graph that represents a query string with any number of edit operations and we show that is is NP-complete, even when labels have length one and in the case the alphabet is binary. Moreover, when it is parameterized by the length of the input string and graph labels have length one, we show that the problem is fixed-parameter tractable and it is unlikely to admit a polynomial kernel. The NP-completeness of this problem leads to the inapproximability (within any factor) of the approximate matching when edit operations are allowed only on the graph labels. Moreover, we show that the variants of approximate string matching to graph we consider are not fixed-parameter tractable, when the parameter is the number of edit operations, even for graphs that have distance one from a DAG. The reduction for this latter result allows us to prove the inapproximability of the variant where edit operations can be applied both on the query string and on graph labels., Comment: Extended version of a paper accepted to LATA 2020

Ever since the introduction of behavioral equivalences on processes one has been searching for efficient proof techniques that accompany those equivalences. Both strong bisimilarity and weak bisimilarity are accompanied by an arsenal of up-to techniques: enhancements of their proof methods. For branching bisimilarity, these results have not been established yet. We show that a powerful proof technique is sound for branching bisimilarity by combining the three techniques of up to union, up to expansion and up to context for Bloom’s BB cool format. We then make an initial proposal for casting the correctness proof of the up to context technique in an abstract coalgebraic setting, covering branching but also, delay and weak bisimilarity.

Castelli, M., Dondi, R., Mauri, G., & Zoppis, I. (2019). Comparing incomplete sequences via longest common subsequence. Theoretical Computer Science, 796, 272-285. https://doi.org/10.1016/j.tcs.2019.09.022 Inspired by scaffold filling, a recent approach for genome reconstruction from incomplete data, we consider a variant of the well-known longest common subsequence problem for the comparison of two sequences. The new problem, called Longest Filled Common Subsequence, aims to compare a complete sequence with an incomplete one, i.e. with some missing elements. Longest Filled Common Subsequence (LFCS), given a complete sequence A, an incomplete sequence B, and a multiset M of symbols missing in B, asks for a sequence B⁎ obtained by inserting the symbols of M into B so that B⁎ induces a common subsequence with A of maximum length. We investigate the computational and approximation complexity of the problem and we show that it is NP-hard and APX-hard when A contains at most two occurrences of each symbol, and we give a polynomial time algorithm when the input sequences are over a constant-size alphabet. We give a [Formula presented] approximation algorithm for the Longest Filled Common Subsequence problem. Finally, we present a fixed-parameter algorithm for the problem, when it is parameterized by the number of symbols inserted in B that “match” symbols of A. authorsversion published

We consider how the orthology/paralogy information can be corrected in order to represent a gene tree, a problem that has recently gained interest in phylogenomics. Interestingly, the problem is related to the Minimum CoGraph Editing problem on the relation graph that represents orthology/paralogy information, where we want to minimize the number of edit operations on the given relation graph in order to obtain a cograph. In this paper we provide both theoretical and experimental results on the Minimum CoGraph Editing problem. On the theoretical side, we provide approximation algorithms for bounded degree relation graphs, for the general problem and for the problem restricted to deletion of edges. On the experimental side, we present a genetic algorithm for Minimum CoGraph Editing and we provide an experimental evaluation of the genetic algorithm on synthetic data.

Patients who survive brain injuries may develop Disorders of Consciousness (DOC) such as Coma, Vegetative State (VS) or Minimally Conscious State (MCS). Unfortunately, the rate of misdiagnosis between VS and MCS due to clinical judgment is high. Therefore, diagnostic decision support systems aiming to correct any differentiation between VS and MCS are essential for the characterization of an adequate treatment and an effective prognosis. In recent decades, there has been a growing interest in the new EEG computational techniques. We have reviewed how resting-state EEG is computationally analyzed to support differential diagnosis between VS and MCS in view of applicability of these methods in clinical practice. The studies available so far have used different techniques and analyses; it is therefore hard to draw general conclusions. Studies using a discriminant analysis with a combination of various factors and reporting a cut-off are among the most interesting ones for a future clinical application.

We study a variant of the problem of finding a collection of disjoint s-clubs in a given network. Given a graph, the problem asks whether there exists a collection of at most r disjoint s-clubs that covers at least k vertices of the network. An s-club is a connected graph that has diameter bounded by s, for a positive integer s. We demand that each club is non-trivial, that is it has order at least t ≥ 2 , for some positive integer t. We prove that the problem is APX-hard even when the input graph has bounded degree, s = 2 , t = 3 and r = | V | . Moreover, we show that the problem is polynomial-time solvable when s ≥ 4 , t = 3 and r = | V | , and when s ≥ 3 , t = 2 and r = | V | . Finally, for s ≥ 2 , we present a fixed-parameter algorithm for the problem, when parameterized by the number of covered vertices.

Support Vector Machines (SVMs) and Kernel methods have found a natural and effective coexistence since their introduction in the early 90s. In this article, we will describe the main concepts that motivate the importance of this relationship. In fact SVMs use kernels for learning linear predictors in high dimensional feature spaces. First, we will describe intuitively how this mechanism is realized, introducing the main concepts and definitions, i.e., maximum margin hyperplane, kernels and non-linearly separable problems. Then the main mathematical issues for linear and nonlinear SVM-based classification will be detailed. We will also introduce some important extensions of the SVMs ideas, by considering the Soft Margin Classification, SVM multi-class classification, SVM clustering, and SVM regression.

International audience; Finding cohesive subgraphs in a network has been investigated in many network mining applications. Several alternative formulations of cohesive subgraph have been proposed, a notable one of them is s-club, which is a subgraph whose diameter is at most s. Here we consider a natural variant of the well-known Minimum Clique Cover problem, where we aim to cover a given graph with the minimum number of s-clubs, instead of cliques. We study the computational and approximation complexity of this problem, when s is equal to 2 or 3. We show that deciding if there exists a cover of a graph with three 2-clubs is NP-complete, and that deciding if there exists a cover of a graph with two 3-clubs is NP-complete. Then, we consider the approximation complexity of covering a graph with the minimum number of 2-clubs and 3-clubs. We show that, given a graph G=(V,E) to be covered, covering G with the minimum number of 2-clubs is not approximable within factor O(|V|1/2−ε), for any ε>0, and covering G with the minimum number of 3-clubs is not approximable within factor O(|V|1−ε), for any ε>0. On the positive side, we give an approximation algorithm of factor 2|V|1/2log3/2|V| for covering a graph with the minimum number of 2-clubs.

Kernels are a type of similarity measures between observed patterns. By exploiting an important mathematical property, they provide new pattern representation and, at the same time, new perspectives to solve many machine learning problems. In this article, we will describe and motivate the main idea of the kernel approach. Notice that, while the usage of kernels is based on well founded theoretical arguments, we will confine our discussion to the main intuitive functional concepts and definitions.

Recommender Systems have became extremely appealing for all technology enhanced learning researches aimed to design, develop and test technical innovations which support and enhance learning and teaching practices of both individuals and organizations. In this scenario a new emerging paradigm of explainable Recommander Systems leverages social friend information to provide (social) explanations in order to supply users with his/her friends’ public interests as explained recommendation. In this paper we introduce our educational platform called “WhoTeach”, an innovative and original system to integrate knowledge discovery, social networks analysis, and educational services. In particular, we report here our work in progress for providing “WhoTeach” environment with optimized Social Explainable Recommandations oriented to design new teachers’ programmes and courses.

In this contribution, we describe the main graph algorithms that are applied in several fields, from transport network to computational biology. First, we will review two-well known traversal algorithms (depth-first search and breadth-first search). Then we consider the problem of computing a shortest path between two vertices and we review the Dijkstra's algorithm, the Bellman-Ford algorithm and Floyd-Warshall algorithm. Another fundamental graph problem we will deal with is that of computing a maximum flow in graph and we will review the Ford-Fulkerson algorithm for the computation of a maximum flow. Next, we will consider consider the computation of a minimum spanning tree of a given graph, and we will review two well-know algorithms for solving this problem: Kruskal's algorithm and Prim's algorithm. Finally, we will consider the traveling salesman problem and the nearest neighbour algorithm, which is a heuristic for this problem.

The identification of cohesive communities (dense sub-graphs) is a typical task applied to the analysis of social and biological networks. Different definitions of communities have been adopted for particular occurrences. One of these, the 2-club (dense subgraphs with diameter value at most of length 2) has been revealed of interest for applications and theoretical studies. Unfortunately, the identification of 2-clubs is a computationally intractable problem, and the search of approximate solutions (at a reasonable time) is therefore fundamental in many practical areas. In this article, we present a genetic algorithm based heuristic to compute a collection of Top k 2-clubs, i.e., a set composed by the largest k 2-clubs which cover an input graph. In particular, we discuss some preliminary results for synthetic data obtained by sampling Erdös-Rényi random graphs.

Gene tree correction has recently gained interest in phylogenomics, as it gives insights in understanding the evolution of gene families. Following some recent approaches based on leaf edit operations, we consider a variant of the problem where a gene tree is corrected by inserting leaves with labels in a multiset M. We show that the problem of deciding whether a gene tree can be corrected by inserting leaves with labels in M is NP-complete. Then, we consider an optimization variant of the problem that asks for the correction of a gene tree with leaves labeled by a multiset M ′ , with M ′ ⊇ M , having minimum size. For this optimization variant of the problem, we present a factor 2 approximation algorithm.

Finding cohesive subgraphs in a network is a well-known problem in graph theory. Several alternative formulations of cohesive subgraph have been proposed, a notable example being $s$-club, which is a subgraph where each vertex is at distance at most $s$ to the others. Here we consider the problem of covering a given graph with the minimum number of $s$-clubs. We study the computational and approximation complexity of this problem, when $s$ is equal to 2 or 3. First, we show that deciding if there exists a cover of a graph with three $2$-clubs is NP-complete, and that deciding if there exists a cover of a graph with two $3$-clubs is NP-complete. Then, we consider the approximation complexity of covering a graph with the minimum number of $2$-clubs and $3$-clubs. We show that, given a graph $G=(V,E)$ to be covered, covering $G$ with the minimum number of $2$-clubs is not approximable within factor $O(|V|^{1/2 -\varepsilon})$, for any $\varepsilon>0$, and covering $G$ with the minimum number of $3$-clubs is not approximable within factor $O(|V|^{1 -\varepsilon})$, for any $\varepsilon>0$. On the positive side, we give an approximation algorithm of factor $2|V|^{1/2}\log^{3/2} |V|$ for covering a graph with the minimum number of $2$-clubs., Accepted in IWOCA 2018

Social interaction allows to support the disease management by creating online spaces where patients can interact with clinicians, and share experiences with other patients. Therefore, promoting targeted communication in online social spaces is a means to group patients around shared goals, offer emotional support, and finally engage patients in their healthcare decision making process. In this paper, we approach the argument from a theoretical perspective: we design an optimization problem aimed to encourage the creation of (induced) sub-networks of patients which, being recently diagnosed, wish to deepen the knowledge about their medical treatment with some other similar profiled patients, which have already been followed up by specific (even alternative) care centers. In particular, due to the computational hardness of the proposed problem, we provide approximated solutions based on distributed heuristics (i.e., Genetic Algorithms). Results are given for simulated data using Erdos-Renyi random graphs.

Agapito, G., Cannataro, M., Castelli, M., Dondi, R., & Zoppis, I. (2017). 10th Workshop on Biomedical and Bioinformatics Challenges for Computer Science - BBC2017. Procedia Computer Science, 108, 1113-1114. https://doi.org/10.1016/j.procs.2017.05.279

Motivation: Haplotype assembly is the computational problem of reconstructing haplotypes in diploid organisms and is of fundamental importance for characterizing the effects of single-nucleotide polymorphisms on the expression of phenotypic traits. Haplotype assembly highly benefits from the advent of ‘future-generation’ sequencing technologies and their capability to produce long reads at increasing coverage. Existing methods are not able to deal with such data in a fully satisfactory way, either because accuracy or performances degrade as read length and sequencing coverage increase or because they are based on restrictive assumptions. Results: By exploiting a feature of future-generation technologies—the uniform distribution of sequencing errors—we designed an exact algorithm, called HapCol, that is exponential in the maximum number of corrections for each single-nucleotide polymorphism position and that minimizes the overall error-correction score. We performed an experimental analysis, comparing HapCol with the current state-of-the-art combinatorial methods both on real and simulated data. On a standard benchmark of real data, we show that HapCol is competitive with state-of-the-art methods, improving the accuracy and the number of phased positions. Furthermore, experiments on realistically simulated datasets revealed that HapCol requires significantly less computing resources, especially memory. Thanks to its computational efficiency, HapCol can overcome the limits of previous approaches, allowing to phase datasets with higher coverage and without the traditional all-heterozygous assumption. Availability and implementation: Our source code is available under the terms of the GNU General Public License at http://hapcol.algolab.eu/. Contact: bonizzoni@disco.unimib.it Supplementary information: Supplementary data are available at Bioinformatics online.

We present a graph-based approach to support case vs control discrimination problems. The goal is to partition a given input graph in two sets, a clique and an independent set, such that there is no edge connecting a vertex of the clique with a vertex of the independent set. Following a parsimonious principle, we consider the problem that aims to modify the input graph into a most similar output graph that consists of a clique and an independent set (with no edge between the two sets). First, we present a theoretical result showing that the problem admits a polynomial-time approximation scheme. Then, motivated by the complexity of such an algorithm, we propose a genetic algorithm and we present an experimental analysis on simulated data.

In diploid genomes, haplotype assembly is the computational problem of reconstructing the two parental copies, called haplotypes, of each chromosome starting from sequencing reads, called fragments, possibly affected by sequencing errors. Minimum error correction (MEC) is a prominent computational problem for haplotype assembly and, given a set of fragments, aims at reconstructing the two haplotypes by applying the minimum number of base corrections. MEC is computationally hard to solve, but some approximation-based or fixed-parameter approaches have been proved capable of obtaining accurate results on real data. In this work, we expand the current characterization of the computational complexity of MEC from the approximation and the fixed-parameter tractability point of view. In particular, we show that MEC is not approximable within a constant factor, whereas it is approximable within a logarithmic factor in the size of the input. Furthermore, we answer open questions on the fixed-parameter tractability for parameters of classical or practical interest: the total number of corrections and the fragment length. In addition, we present a direct 2-approximation algorithm for a variant of the problem that has also been applied in the framework of clustering data. Finally, since polyploid genomes, such as those of plants and fishes, are composed of more than two copies of the chromosomes, we introduce a novel formulation of MEC, namely the k-ploid MEC problem, that extends the traditional problem to deal with polyploid genomes. We show that the novel formulation is still both computationally hard and hard to approximate. Nonetheless, from the parameterized point of view, we prove that the problem is tractable for parameters of practical interest such as the number of haplotypes and the coverage, or the number of haplotypes and the fragment length.

The Correlation Clustering problem has been introduced recently [N. Bansal, A. Blum, S. Chawla, Correlation Clustering, in: Proc. 43rd Symp. Foundations of Computer Science, FOCS, 2002, pp. 238-247] as a model for clustering data when a binary relationship between data points is known. More precisely, for each pair of points we have two scores measuring the similarity and dissimilarity respectively, of the two points, and we would like to compute an optimal partition where the value of a partition is obtained by summing up the similarity scores of pairs involving points from the same cluster and the dissimilarity scores of pairs involving points from different clusters. A closely related problem is Consensus Clustering, where we are given a set of partitions and we would like to obtain a partition that best summarizes the input partitions. The latter problem is a restricted case of Correlation Clustering. In this paper we prove that Minimum Consensus Clustering is APX-hard even for three input partitions, answering an open question in the literature, while Maximum Consensus Clustering admits a PTAS. We exhibit a combinatorial and practical frac(4, 5)-approximation algorithm based on a greedy technique for Maximum Consensus Clustering on three partitions. Moreover, we prove that a PTAS exists for Maximum Correlation Clustering when the maximum ratio between two scores is at most a constant. © 2007 Elsevier Inc. All rights reserved.

International audience; The new sequencing technologies, called next-generation se-quencing, provide a huge amount of data that can be used to reconstruct genomes. However, the methods applied to reconstruct genomes often are not able to reconstruct a complete genome and provide only an incomplete information. Here we consider two combinatorial problems that aim to reconstruct complete genomes by inserting a collection of missing genes. The first problem we consider, called One-sided scaffold filling, given an incomplete genome B and a complete genome A, asks for the insertion of missing genes into an incomplete genome B with the goal of maximizing the common adjacencies between genomes B (resulting from the insertion of missing genes in B) and A. The second problem, called Two-sided scaffold filling, given two incomplete genomes A, B, asks for the insertion of missing genes into both genomes so that the resulting genomes A and B have the same multiset of genes and the number of common adjacencies between A and B is maximized. Both problems were proved to be NP-hard, while their parameterized complexity, when the parameter is the number of common adjacencies of the resulting genomes, was left as an open problem. In this paper, we settle this open problem by presenting fixed-parameter algorithms for One-sided scaffold filling and Two-sided scaffold filling.

International audience; Haplotype assembly is the computational problem of reconstructing the two parental copies, called haplotypes, of each chromosome starting from sequencing reads, called fragments, possibly affected by sequencing errors. Minimum Error Correction (MEC) is a prominent computational problem for haplotype assembly and, given a set of fragments , aims at reconstructing the two haplotypes by applying the minimum number of base corrections. By using novel combinatorial properties of MEC instances, we are able to provide new results on the fixed-parameter tractability and approx-imability of MEC. In particular, we show that MEC is in FPT when para-meterized by the number of corrections, and, on " gapless " instances, it is in FPT also when parameterized by the length of the fragments, whereas the result known in literature forces the reconstruction of complementary haplotypes. Then, we show that MEC cannot be approximated within any constant factor while it is approximable within factor O(log nm) where nm is the size of the input. Finally, we provide a practical 2-approximation algorithm for the Binary MEC, a variant of MEC that has been applied in the framework of clustering binary data.

The Computer Journal, 58 (7), ISSN:0010-4620, ISSN:1460-2067

In several areas, for example in bioinformatics and in AI planning, the Shortest Common Superstring problem (SCS) and variants thereof have been successfully applied for string comparison. In this paper we consider two variants of SCS recently introduced, namely Restricted Common Superstring (RCS) and Swapped Common Superstring (SRCS). In RCS we are given a set $$S$$S of strings and a multiset $$\mathcal {M}$$M of symbols, and we look for an ordering $$\mathcal {M}_o$$Mo of $$\mathcal {M}$$M such that the number of input strings which are substrings of $$\mathcal {M}_o$$Mo is maximized. In SRCS we are given a set $$S$$S of strings and a text $$\mathcal {T}$$T, and we look for a swap ordering $$\mathcal {T}_o$$To of $$\mathcal {T}$$T (an ordering of $$\mathcal {T}$$T obtained by swapping only some pairs of adjacent symbols) such that the number of input strings which are substrings of $$\mathcal {T}_o$$To is maximized. In this paper we propose a multivariate algorithmic analysis of the complexity of the two problems, aiming at determining how different parameters influence the complexity of the two problems. We consider as interesting parameters the size of the solutions (that is the number of input strings contained in the computed superstring), the maximum length of the given input strings, the size of the alphabet over which the input strings range. First, we give two fixed-parameter algorithms, where the parameter is the size of the solution, for SRCS and lRCS (the RCS problem restricted to strings of length bounded by a parameter $$\ell $$l). Furthermore, we complement these results by showing that SRCS and lRCS do not admit a polynomial kernel unless $$NP \subseteq coNP/Poly$$NP⊆coNP/Poly. Then, we show that SRCS is APX-hard even when the input strings have length bounded by a constant (equal to $$10$$10) or are over a binary alphabet.

When tens and even hundreds of schemas are involved in the integration process, criteria are needed for choosing clusters of schemas to be integrated, so as to deal with the integration problem through an efficient iterative process. Schemas in clusters should be chosen according to cohesion and coupling criteria that are based on similarities and dissimilarities among schemas. In this paper, we propose an algorithm for a novel variant of the correlation clustering approach that addresses the problem of assisting a designer in integrating a large number of conceptual schemas. The novel variant introduces upper and lower bounds to the number of schemas in each cluster, in order to avoid too complex and too simple integration contexts respectively. We give a heuristic for solving the problem, being an NP hard combinatorial problem. An experimental activity demonstrates an appreciable increment in the effectiveness of the schema integration process when clusters are computed by means of the proposed algorithm w.r.t. the ones manually defined by an expert.

A central issue in biological data analysis is that uncertainty, resulting from different factors of variability, may change the effect of the events being investigated. Therefore, robustness is a fundamental step to be considered. Robustness refers to the ability of a process to cope well with uncertainties, but the different ways to model both the processes and the uncertainties lead to many alternative conclusions in the robustness analysis. In this paper we apply a framework allowing to deal with such questions for mass spectrometry data. Specifically, we provide robust decisions when testing hypothesis over a case/control population of subject measurements (i.e. proteomic profiles). To this concern, we formulate (i) a reference model for the observed data (i.e., graphs), (ii) a reference method to provide decisions (i.e., test of hypotheses over graph properties) and (iii) a reference model of variability to employ sources of uncertainties (i.e., random graphs). We apply these models to a realcase study, analyzing the mass spectrometry profiles of the most common type of Renal Cell Carcinoma; the Clear Cell variant.

Gene tree correction with respect to a given species tree is a problem that has been recently proposed in order to better understand the evolution of gene families. One of the combinatorial methods proposed to tackle with this problem aims to correct a gene tree by removing the minimum number of leaves/labels (Minimum Leaf Removal and Minimum Label Removal, respectively). The two problems have been shown to be APX-hard, and fixed-parameter tractable, when parameterized by the number of leaves/labels removed. In this paper, we focus on the approximation complexity of these two problems and we show that they are not approximable within factor b log ? m , where m is the number of leaves of the species tree and b 0 is a constant. Furthermore, we introduce and study two new variants of the problem, where the goal is the correction of a gene tree with the minimum number of leaf/label modifications (Minimum Leaf Modification and Minimum Label Modification, respectively). We show that the two modification problems, differently from the removal versions, are unlikely to be fixed-parameter tractable. More precisely, we prove that the Minimum Leaf Modification problem is W 1 ] -hard, when parameterized by the number of leaf modifications, and that the Minimum Label Modification problem is W 2 ] -hard, when parameterized by the number of label modifications.

The general problem of reconciling the information from evolutionary trees representing the relationships between distinct gene families is of great importance in bioinformatics and has been popularized among the computer science researchers by Ma et al. [From gene trees to species trees, SIAM J. Comput. 30(3) (2000) 729–752] where the authors pose the intriguing question if a certain definition of minimum tree that reconciles a gene tree and a species tree is correct. We answer affirmatively to this question; moreover, we show an efficient algorithm for computing such minimum-leaf reconciliation trees and prove the uniqueness of such trees. We then tackle some different versions of the biological problem by showing that the exemplar problem, arising from the exemplar analysis of multigene genomes, is NP-hard even when the number of copies of a given label is at most two. Finally, we introduce two novel formulations for the problem of recombining evolutionary trees, extending the gene duplication problem studied in [Ma et al., From gene trees to species trees, SIAM J. Comput. 30(3) (2000) 729–752; M. Fellows et al., On the multiple gene duplication problem, in: Proc. Ninth Internat. Symp. on Algorithms and Computation (ISAAC98), 1998; R. Page, Maps between trees and cladistic analysis of historical associations among genes, Systematic Biology 43 (1994) 58–77; R.M. Page, J. Cotton, Vertebrate phylogenomics: reconciled trees and gene duplications, in: Proc. Pacific Symp. on Biocomputing 2002 (PSB2002), 2002, pp. 536–547; R. Guigò et al., Reconstruction of ancient molecular phylogeny, Mol. Phy. and Evol. 6(2) (1996) 189–213], and we give an exact algorithm (via dynamic programming) for one of these formulations.