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Finding heavy-elements (heavy-hitters) in streaming data is one of the central, and well-understood tasks. Despite the importance of this problem, when considering the sliding windows model of streaming (where elements eventually expire) the problem of finding L 2 -heavy elements has remained completely open despite multiple papers and considerable success in finding L 1 -heavy elements. Since the L 2 -heavy element problem doesn't satisfy certain conditions, existing methods for sliding windows algorithms, such as smooth histograms or exponential histograms are not directly applicable to it. In this paper, we develop the first polylogarithmic-memory algorithm for finding L 2 -heavy elements in the sliding window model. Our technique allows us not only to find L 2 -heavy elements, but also heavy elements with respect to any L p with 0 < p ≤ 2 on sliding windows. By this we completely “close the gap” and resolve the question of finding L p -heavy elements in the sliding window model with polylogarithmic memory, since it is well known that for p > 2 this task is impossible. We demonstrate a broader applicability of our method on two additional examples: we show how to obtain a sliding window approximation of the similarity of two streams, and of the fraction of elements that appear exactly a specified number of times within the window (the α -rarity problem). In these two illustrative examples of our method, we replace the current expected memory bounds with worst case bounds. [ABSTRACT FROM AUTHOR]

Abstract: Associative-classification is a promising classification method based on association-rule mining. Significant amount of work has already been dedicated to the process of building a classifier based on association rules. However, relatively small amount of research has been performed in association-rule mining from multi-label data. In such data each example can belong, and thus should be classified, to more than one class. This paper aims at the most demanding, with respect to computational cost, part in associative-classification, which is efficient generation of association rules. This task can be achieved using different frequent pattern mining methods. In this paper, we propose a new method that is based on the state-of-the-art tree-projection-based frequent pattern mining algorithm. This algorithm is modified to improve its efficiency and extended to accommodate the multi-label recurrent-item associative-classification rule generation. The proposed algorithm is tested and compared with A priori-based associative-classification rule generator on two large datasets. [Copyright &y& Elsevier]

Abstract: Katriel and Bodlaender [Irit Katriel, Hans L. Bodlaender, Online topological ordering, ACM Transactions on Algorithms 2 (3) (2006) 364–379] modify the algorithm proposed by Alpern et al. [Bowen Alpern, Roger Hoover, Barry K. Rosen, Peter F. Sweeney, F. Kenneth Zadeck, Incremental evaluation of computational circuits, in: Proceedings of the First Annual ACM–SIAM Symposium on Discrete Algorithms (SODA), 1990, pp. 32–42] for maintaining the topological order of the nodes of a directed acyclic graph while inserting edges and prove that their algorithm runs in time and has an lower bound. In this paper, we give a tight analysis of their algorithm by showing that it runs in time 1 [1] In this paper, we assume that . In fact, our analysis can be easily extended to prove that the algorithm runs in time without the assumption . . [Copyright &y& Elsevier]

The advice complexity of an online problem describes the additional information both necessary and sufficient for online algorithms to compute solutions of a certain quality. In this model, an oracle inspects the input before it is processed by an online algorithm. Depending on the input string, the oracle prepares an advice bit string that is accessed sequentially by the algorithm. The number of advice bits that are read to achieve some specific solution quality can then serve as a fine-grained complexity measure. The main contribution of this paper is to study a powerful method for proving lower bounds on the number of advice bits necessary. To this end, we consider the string guessing problem as a generic online problem and show a lower bound on the number of advice bits needed to obtain a good solution. We use special reductions from string guessing to improve the best known lower bound for the online set cover problem and to give a lower bound on the advice complexity of the online maximum clique problem. [ABSTRACT FROM AUTHOR]

This paper presents a practical decision procedure for Propositional Projection Temporal Logic with infinite models. First, a set Prop l of labels l i , 0 ⩽ i ⩽ n ∈ N 0 , is used to mark nodes of an LNFG of a formula, and a node with l i is treated as an accepting state as in an automaton. Further, the generalized Büchi accepting condition for automata is employed to identify a path (resulting a word) in an LNFG as a model of the formula. In addition, the implementation details of the decision procedure and relevant algorithms including pre-processing, LNFG, circle finding algorithms are presented; as a matter of fact, all algorithms are implemented by C++ programs. [ABSTRACT FROM AUTHOR]

The Maximum Agreement Forest problem ( MAF ) asks for a largest common subforest of a collection of phylogenetic trees. The MAF problem on two binary phylogenetic trees has been studied extensively in the literature. In this paper, we present a group of fixed-parameter tractable algorithms for the MAF problem on multiple (i.e., two or more) binary phylogenetic trees. Our techniques work fine for the problem for both rooted trees and unrooted trees. The computational complexity of our algorithms is comparable with that of the known algorithms for two trees, and is independent of the number of phylogenetic trees for which a maximum agreement forest is constructed. [ABSTRACT FROM AUTHOR]

Given a connected outerplanar graph G of pathwidth p , we give an algorithm to add edges to G to get a supergraph of G , which is 2-vertex-connected, outerplanar and of pathwidth O ( p ) . This settles an open problem raised by Biedl [1] , in the context of computing minimum height planar straight line drawings of outerplanar graphs, with their vertices placed on a two-dimensional grid. In conjunction with the result of this paper, the constant factor approximation algorithm for this problem obtained by Biedl [1] for 2-vertex-connected outerplanar graphs will work for all outer planar graphs. [ABSTRACT FROM AUTHOR]

Abstract: Text steam analysis is now of great importance and practical value today. It has several applications such as news group filtering, topic detection & tracking (TDT), user characterized recommendation etc. Clustering is one of the most important methods of analyzing text stream. However, most text stream clustering algorithms rarely consider the possible change of features during a long-time of clustering, which is usually the case, leading to unsatisfactory results of the clustering system. The paper mainly focuses on the problem of adaptive feature selection for clustering text stream. A validity index based method of adaptive feature selection is proposed, incorporating with which a new text stream clustering algorithm is developed. During the clustering process, threshold of cluster valid index is used to automatically trigger feature re-selection in order to ensure the validity of clustering. The experiment using Reuters-21578 text set as the text source shows that the clustering algorithm reaches reasonable results of high quality. [ABSTRACT FROM AUTHOR]

Abstract: For a set of points (terminals) in the plane, a Manhattan network on is a network with the property that its edges are horizontal or vertical segments connecting points in and for every pair of terminals, the network contains a shortest -path between them. A minimum Manhattan network on is a Manhattan network of minimum possible length. The problem of finding minimum Manhattan networks has been introduced by Gudmundsson, Levcopoulos, and Narasimhan [J. Gudmundsson, C. Levcopoulos, G. Narasimhan, Approximating a minimum Manhattan network, Nordic Journal of Computing 8 (2001) 219–232. Proc. APPROX’99, 1999, pp. 28–37] and its complexity status is unknown. Several approximation algorithms (with factors 8, 4, and 3) have been proposed; recently Kato, Imai, and Asano [R. Kato, K. Imai, T. Asano, An improved algorithm for the minimum Manhattan network problem, ISAAC’02, in: LNCS, vol. 2518, 2002, pp. 344–356] have given a factor 2-approximation algorithm, however their correctness proof is incomplete. In this paper, we propose a rounding 2-approximation algorithm based on an LP-formulation of the minimum Manhattan network problem. [Copyright &y& Elsevier]

Abstract: Let be a connected graph such that each edge is weighted by nonnegative real . Let be a vertex designated as a source, be a positive integer, and be a set of terminals. The capacitated multicast tree routing problem (CMTR) asks to find a partition of and a set of trees of such that consists of at most terminals and each spans . The objective is to minimize , where denotes the sum of weights of all edges in . In this paper, we propose a -approximation algorithm to the CMTR, where is the best achievable approximation ratio for the Steiner tree problem. [Copyright &y& Elsevier]

Abstract: In this paper, we study the problem of finding the shortest path between two points inside a simple polygon such that there is at least one point on the path from which a query point is visible. We provide an algorithm which preprocesses the input in time and space and provides logarithmic query time. The input polygon has vertices and is a parameter dependent on the input polygon which is in the worst case but is much smaller for most polygons. The preprocessing algorithm sweeps an angular interval around every reflex vertex of the polygon to store the optimal contact points between the shortest paths and the windows separating the visibility polygons of the query points from the source and the destination. [Copyright &y& Elsevier]