In this paper, we use the primeval decomposition tree to compute the minimal separators of some graphs and to describe a linear-time algorithm that lists the minimal separators of extended P-4-laden graphs, extending ...
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In this paper, we use the primeval decomposition tree to compute the minimal separators of some graphs and to describe a linear-time algorithm that lists the minimal separators of extended P-4-laden graphs, extending an algorithm for P-4-sparse graphs given by Nikolopoulos and Palios [S.D. Nikolopoulos, L Palios, Minimal separators in P-4-sparse graphs, Discrete Math. 306 (3) (2006) 381-392]. We also give bounds on the number and total size of all minimal separators of extended P-4-laden graphs and some of their subclasses, such as P-4-tidy and P-4-lite graphs. Moreover, we show that these bounds are tight for all subclasses considered. (C) 2012 Elsevier B.V. All rights reserved.
Phylogenetic networks are used to represent evolutionary scenarios in biology and linguistics. To find the most probable scenario, it may be necessary to compare candidate networks. In particular, one needs to disting...
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Phylogenetic networks are used to represent evolutionary scenarios in biology and linguistics. To find the most probable scenario, it may be necessary to compare candidate networks. In particular, one needs to distinguish different networks and determine whether one network is contained in another. In this paper, we introduce cherry-picking networks, a class of networks that can be reduced by a so-called cherry-picking sequence. We then show how to compare such networks using their sequences. We characterize reconstructible cherry-picking networks, which are the networks that are uniquely determined by the sequences that reduce them, making them distinguishable. Furthermore, we show that a cherry-picking network is contained in another cherry picking network if a sequence for the latter network reduces the former network, provided both networks can be reconstructed from their sequences in a similar way (i.e., they are in the same reconstructible class). Lastly, we show that the converse of the above statement holds for tree-child networks, thereby showing that NETWORK CONTAINMENT, the problem of checking whether a network is contained in another, can be solved by computing cherry picking sequences in lineartime for tree-child networks. (C) 2020 The Author(s). Published by Elsevier B.V.
A cograph completion of an arbitrary graph G is a cograph supergraph of G on the same vertex set. Such a completion is called minimal if the set of edges added to G is inclusion minimal. In this paper we present two r...
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A cograph completion of an arbitrary graph G is a cograph supergraph of G on the same vertex set. Such a completion is called minimal if the set of edges added to G is inclusion minimal. In this paper we present two results on minimal cograph completions. The first is a characterization that allows us to check in lineartime whether a given cograph completion is minimal. The second result is a vertex incremental algorithm to compute a minimal cograph completion H of an arbitrary input graph G in O(vertical bar V(H)vertical bar + vertical bar E(H)vertical bar) time. An extended abstract of the result has been already presented at FAW 2008 [D. Lokshtanov, F. Mancini, C. Papadopoulos, Characterizing and computing minimal cograph completions, ill: Proceedings of FAW'08-2nd International Frontiers of Algorithmics Workshop, in: LNCS, vol. 5059, 2008, pp. 147-158. [1]]. (c) 2009 Elsevier B.V. All rights reserved.
Let G = (V, E) be a graph without isolated vertices A matching in G 2,5 a set of independent edges in G A perfect matching M in G is a matching such that every vertex of G is incident to an edge of M A set S subset of...
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Let G = (V, E) be a graph without isolated vertices A matching in G 2,5 a set of independent edges in G A perfect matching M in G is a matching such that every vertex of G is incident to an edge of M A set S subset of V is a paired-dominating set of G if every vertex not in S is adjacent to a vertex in S, and if the subgraph induced by S contains a perfect matching The paired-domination problem is to find a paired-dominating set of G with minimum cardinality This paper introduces a generalization of the paired-domination problem, namely, the restricted paired domination problem, where some vertices are restricted so as to be in paired dominating sets Further, possible applications are also presented We then present a linear-time constructive algorithm to solve the restricted paired domination problem in cographs
Many different index structures, providing efficient solutions to problems related to pattern matching, have been introduced so far. Examples of these structures are suffix trees and directed acyclic word graphs (DAWG...
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Many different index structures, providing efficient solutions to problems related to pattern matching, have been introduced so far. Examples of these structures are suffix trees and directed acyclic word graphs (DAWGs), which can be efficiently constructed in lineartime and space. Compact directed acyclic word graphs (CDAWGs) are an index structure preserving some features of both suffix trees and DAWGs, and require less space than both of them. An algorithm which directly constructs CDAWGs in lineartime and space was first introduced by Crochemore and Verin, based on McCreight's algorithm for constructing suffix trees. In this work, we present a novel on-line linear-time algorithm that builds the CDAWG for a single string as well as for a set of strings, inspired by Ukkonen's on-line algorithm for constructing suffix trees. (C) 2004 Elsevier B.V. All rights reserved.
The subject of the paper is to propose an O(Absolute value of V + Absolute value of E) algorithm for the 3-edge-connectivity augmentation problem (UW-3-ECA) defined by ''Given an undirected graph G0 = (V, E), ...
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The subject of the paper is to propose an O(Absolute value of V + Absolute value of E) algorithm for the 3-edge-connectivity augmentation problem (UW-3-ECA) defined by ''Given an undirected graph G0 = (V, E), find an edge set E' of minimum cardinality such that the graph (V,E or E') (denoted as G0 + E') is 3-edge-connected, where each edge of E' connects distinct vertices of V.'' Such a set E' is called a solution to the problem. Let UW-3-ECA(S) (UW-3-ECA(M), respectively) denote UW-3-ECA in which G0 + E' is required to be simple (G0 + E' may have multiple edges). Note that we can assume that G0 is simple in UW-3-ECA(S). UW-3-ECA(M) is divided into two subproblems (1) and (2) as follows: (1) finding all k-edge-connected components of a given graph for every k less-than-or-equal-to 3, and (2) determining a minimum set of edges whose addition to 66 result in a 3-edge-connected graph. Concerning the subproblem (1), we use an O(Absolute value of V + Absolute value of E) algorithm that has already been existing. The paper proposes an 0 (Absolute value of V + Absolute value of E) algorithm for the subproblem (2). Combining these algorithms makes an O(Absolute value of V + Absolute value of E) algorithm for finding a solution to UW-3-ECA (M). Furthermore, it is shown that a solution E' to UW-3-ECA (M) is also a solution to UW-3-ECA(S) if Absolute value of V greater-than-or-equal-to 4, partly solving an open problem UW-k-ECA(S) that is a generalization of UW-3-ECA (S).
For two matroids M-1 and M-2 defined on the same ground set E, the online matroid intersection problem is to design an algorithm that constructs a large common independent set in an online fashion. The algorithm is pr...
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ISBN:
(纸本)9783319592503;9783319592497
For two matroids M-1 and M-2 defined on the same ground set E, the online matroid intersection problem is to design an algorithm that constructs a large common independent set in an online fashion. The algorithm is presented with the ground set elements one-by-one in a uniformly random order. At each step, the algorithm must irrevocably decide whether to pick the element, while always maintaining a common independent set. While the natural greedy algorithm-pick an element whenever possible-is half competitive, nothing better was previously known;even for the special case of online bipartite matching in the edge arrival model. We present the first randomized online algorithm that has a 1/2 + delta competitive ratio in expectation, where delta > 0 is a constant. The expectation is over the random order and the coin tosses of the algorithm. As a corollary, we also obtain the first lineartime algorithm that beats half competitiveness for offline matroid intersection.
Software watermarking involves integrating an identifier within the software, enabling timely retrieval to disclose authorship/ownership, and deter piracy. Various software watermarking schemes have been proposed in t...
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Many different index structures, providing efficient solutions to problems related to pattern matching, have been introduced so far. Examples of these structures are suffix trees and directed acyclic word graphs (DAWG...
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ISBN:
(数字)9783540481942
ISBN:
(纸本)9783540422716
Many different index structures, providing efficient solutions to problems related to pattern matching, have been introduced so far. Examples of these structures are suffix trees and directed acyclic word graphs (DAWGs), which can be efficiently constructed in lineartime and space. Compact directed acyclic word graphs (CDAWGs) are an index structure preserving some features of both suffix trees and DAWGs, and require less space than both of them. An algorithm which directly constructs CDAWGs in lineartime and space was first introduced by Crochemore and Verin, based on McCreight's algorithm for constructing suffix trees. In this work, we present a novel on-line linear-time algorithm that builds the CDAWG for a single string as well as for a set of strings, inspired by Ukkonen's on-line algorithm for constructing suffix trees. (C) 2004 Elsevier B.V. All rights reserved.
We present a near-lineartime algorithm that approximates the edit distance between two strings within a polylogarithmic factor. For strings of length n and every fixed epsilon > 0, the algorithm computes a (log n)...
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ISBN:
(纸本)9780769542447
We present a near-lineartime algorithm that approximates the edit distance between two strings within a polylogarithmic factor. For strings of length n and every fixed epsilon > 0, the algorithm computes a (log n)(O(1/epsilon)) approximation in n(1+epsilon) time. This is an exponential improvement over the previously known approximation factor, 2((O) over tilde(root log n)), with a comparable running time [Ostrovsky and Rabani, J. ACM 2007;Andoni and Onak, STOC 2009]. This result arises naturally in the study of a new asymmetric query model. In this model, the input consists of two strings x and y, and an algorithm can access y in an unrestricted manner, while being charged for querying every symbol of x. Indeed, we obtain our main result by designing an algorithm that makes a small number of queries in this model. We then provide a nearly-matching lower bound on the number of queries. Our lower bound is the first to expose hardness of edit distance stemming from the input strings being "repetitive", which means that many of their substrings are approximately identical. Consequently, our lower bound provides the first rigorous separation between edit distance and Ulam distance.
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