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The goal of radiotherapy is to cover a target area with a desired radiation dose while keeping the exposition of non-target areas as low as possible in order to reduce radiation side effects. In the case of Intensity Modulated Proton Therapy (IMPT), the dose distribution is typically designed via a treatment planning optimisation process based on classical optimisation algorithms on some objective functions. We investigate the planning optimisation problem under the point of view of the Theory of Complexity in general and, in particular, of the Combinatorial Optimisation Theory. We firstly give a formal definition of a simplified version of the problem that is in the complexity class NPO. We prove that above version is computationally hard, i.e. it belongs to the class NPOnPTAS if NP , P. We show how Combinatorial Optimisation Theory can give valuable tools, both conceptual and practical, in treatment plan definition, opening the way for new deterministic algorithms with bounded time complexity which have to support the technological evolution up to adaptive plans exploiting near real time solutions. [ABSTRACT FROM AUTHOR]

Bacteria classification has been deeply investigated with different tools for many purposes, such as early diagnosis, metagenomics, phylogenetics. Classification methods based on ribosomal DNA sequences are considered a reference in this area. We present a new classificatier for bacteria species based on a dissimilarity measure of purely combinatorial nature. This measure is based on the notion of Minimal Absent Words, a combinatorial definition that recently found applications in bioinformatics. We can therefore incorporate this measure into a probabilistic neural network in order to classify bacteria species. Our approach is motivated by the fact that there is a vast literature on the combinatorics of Minimal Absent Words in relation with the degree of repetitiveness of a sequence. We ran our experiments on a public dataset of Ribosomal RNA Sequences from the complex 16S. Our approach showed a very high score in the accuracy of the classification, proving hence that our method is comparable with the standard tools available for the automatic classification of bacteria species. [ABSTRACT FROM AUTHOR]

Given a set $\mathcal{D}$ of q documents, the Longest Common Substring (LCS) problem asks, for any integer 2 ⩽ k ⩽ q, the longest substring that appears in k documents. LCS is a well-studied problem having a wide range of applications in Bioinformatics: from microarrays to DNA sequences alignments and analysis. This problem has been solved by Hui (2000International Journal of Computer Science and Engineering15 73–76) by using a famous constant-time solution to the Lowest Common Ancestor (LCA) problem in trees coupled with the use of suffix trees.In this article, we present a simple method for solving the LCS problem by using suffix trees (STs) and classical union-find data structures. In turn, we show how this simple algorithm can be adapted in order to work with other space efficient data structures such as the enhanced suffix arrays (ESA) and the compressed suffix tree. [ABSTRACT FROM AUTHOR]

In this paper we consider the problem of computing the longest common abelian factor (LCAF) between two given strings. We present a simple time algorithm, where n is the length of the strings and is the alphabet size, and a sub-quadratic running time solution for the binary string case, both having linear space requirement. Furthermore, we present a modified algorithm applying some interesting tricks and experimentally show that the resulting algorithm runs faster. [ABSTRACT FROM AUTHOR]

In this paper we describe a "light" algorithm for the on-line construction of a small automaton recognising a finite set of words. The algorithm runs in linear time. We carried out good experimental results on real dictionaries, on biological sequences and on the sets of suffixes (resp. factors) of a set of words that shows how our automaton is near to the minimal one. For the suffixes of a text, we propose a modified construction that leads to an even smaller automaton. We moreover construct linear algorithms for the insertion and deletion of a word in a finite set, directly from the constructed automaton. [ABSTRACT FROM AUTHOR]

Mapping reads against a genome sequence is an interesting and useful problem in computational molecular biology and bioinformatics. In this paper, we focus on the problem of indexing a sequence for mapping reads with a single mismatch. We first focus on a simpler problem where the length of the pattern is given beforehand during the data structure construction. This version of the problem is interesting in its own right in the context of the next generation sequencing. In the sequel, we show how to solve the more general problem. In both cases, our algorithm can construct an efficient data structure in time and space and can answer subsequent queries in time. Here, n is the length of the sequence, m is the length of the read, 0<ε<1 and is the optimal output size. [ABSTRACT FROM AUTHOR]