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Maximum agreement and compatible supertrees
- Proceedings of the 15th Combinatorial Pattern Matching Symposium (CPM’O4), volume 3109 of LNCS
, 2004
"... Given a set of leaf-labelled trees with identical leaf sets, the MAST problem, re-spectively MCT problem, consists of finding a largest subset of leaves such that all input trees restricted to these leaves are isomorphic, respectively compatible. In this paper, we propose extensions of these problem ..."
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Cited by 20 (8 self)
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Given a set of leaf-labelled trees with identical leaf sets, the MAST problem, re-spectively MCT problem, consists of finding a largest subset of leaves such that all input trees restricted to these leaves are isomorphic, respectively compatible. In this paper, we propose extensions of these problems to the context of supertree infer-ence, where input trees have non-identical leaf sets. This situation is of particular interest in phylogenetics. The resulting problems are called SMAST and SMCT. A sufficient condition is given that identifies cases where these problems can be solved by resorting to MAST and MCT as subproblems. This condition is met, for instance, when only two input trees are considered. Then we give algorithms for SMAST and SMCT that benefit from the link with the subtree problems. These algorithms run in time linear to the time needed to solve MAST, respectively MCT, on an instance of the same or smaller size. It is shown that arbitrary instances of SMAST and SMCT can be turned in polynomial time into instances composed of trees with a bounded number of leaves. SMAST is shown to be W[2]-hard when the considered parameter is the number of input leaves that have to be removed to obtain the agreement of the input trees. A simlar result holds for SMCT. Moreover, the corresponding optimization prob-lems, that is the complements of SMAST and SMCT, can not be approximated in polynomial time within a constant factor, unless P = NP. These results also hold when the input trees have a bounded number of leaves. The presented results apply to both collections of rooted and unrooted trees. Preprint submitted to Elsevier Science 17 November 2006 1
Fast fixed-parameter tractable algorithms for nontrivial generalizations of Vertex Cover
- Discrete Appl. Math
"... Abstract Our goal in this paper is the development of fast algorithms for recognizing general classes of graphs. We seek algorithms whose complexity can be expressed as a linear function of the graph size plus an exponential function of k, a natural parameter describing the class. In particular, we ..."
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Cited by 15 (0 self)
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Abstract Our goal in this paper is the development of fast algorithms for recognizing general classes of graphs. We seek algorithms whose complexity can be expressed as a linear function of the graph size plus an exponential function of k, a natural parameter describing the class. In particular, we consider the class W k (G), where for each graph G in W k (G), the removal of a set of at most k vertices from G results in a graph in the base graph class G. (If G is the class of edgeless graphs, W k (G) is the class of graphs with bounded vertex cover.) When G is a minor-closed class such that each graph in G has bounded maximum degree, and all obstructions of G (minor-minimal graphs outside G) are connected, we obtain an O( of (k + 1)(k + 2) on the number of vertices in any obstruction of the class of graphs with vertex cover of size at most k. These results are of independent graph-theoretic interest.
Confronting hardness using a hybrid approach
- in SODA, 2006
"... A hybrid algorithm is a collection of heuristics, paired with a polynomial time selector S that runs on the input to decide which heuristic should be executed to solve the problem. Hybrid algorithms are interesting in scenarios where the selector must decide between heuristics that are “good ” with ..."
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Cited by 14 (0 self)
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A hybrid algorithm is a collection of heuristics, paired with a polynomial time selector S that runs on the input to decide which heuristic should be executed to solve the problem. Hybrid algorithms are interesting in scenarios where the selector must decide between heuristics that are “good ” with respect to different complexity measures. In this paper, we focus on hybrid algorithms with a “hardness-defying ” property: for a problem Π, there is a set of complexity measures {mi} whereby Π is known or conjectured to be hard (or unsolvable) for each mi, but for each heuristic hi of the hybrid algorithm, one can give a complexity guarantee for hi on the instances of Π that S selects for hi that is strictly better than mi. For example, we show that for NP-hard problems such as Max-Ek-Lin-p, Longest Path and Minimum Bandwidth, a given instance can either be solved exactly in “sub-exponential ” (2 o(n)) time, or be approximated in polynomial time with an approximation ratio exceeding that of the known or conjectured inapproximability of the problem, assuming P ̸ = NP. We also prove some inherent limitations to the design of hybrid algorithms that arise under the assumption that NP
LTL over integer periodicity constraints
- PROCEEDINGS OF THE 7TH INTERNATIONAL CONFERENCE ON FOUNDATIONS OF SOFTWARE SCIENCE AND COMPUTATION STRUCTURES (FOSSACS), VOLUME 2987 OF LNCS
, 2004
"... Periodicity constraints are used in many logical formalisms, in fragments of Presburger LTL, in calendar logics, and in logics for access control, to quote a few examples. In the paper, we introduce the logic PLTL mod, an extension of Linear-Time Temporal Logic LTL with past-time operators whose a ..."
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Cited by 12 (4 self)
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Periodicity constraints are used in many logical formalisms, in fragments of Presburger LTL, in calendar logics, and in logics for access control, to quote a few examples. In the paper, we introduce the logic PLTL mod, an extension of Linear-Time Temporal Logic LTL with past-time operators whose atomic formulae are defined from a first-order constraint language dealing with periodicity. Although the underlying constraint language is a fragment of Presburger arithmetic shown to admit a pspace-complete satisfiability problem, we establish that PLTL mod model-checking and satisfiability problems remain in pspace as plain LTL (full Presburger LTL is known to be highly undecidable). This is particularly interesting for dealing with periodicity constraints since the language of PLTL mod has a language more concise than existing languages and the temporalization of our first-order language of periodicity constraints has the same worst case complexity as the underlying constraint language. Finally, we show examples of introduction the quantification in the logical language that provide to PLTL mod, expspacecomplete problems. As another application, we establish that the equivalence problem for extended single-string automata, known to express the equality of time granularities, is pspace-complete by designing a reduction from QBF and by using our results for PLTL mod.
Improved Parameterized Complexity of the Maximum Agreement Subtree and . . .
- IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS
, 2006
"... Given a set of evolutionary trees on a same set of taxa, the maximum agreement subtree problem (MAST), respectively maximum compatible tree problem (MCT), consists of finding a largest subset of taxa such that all input trees restricted to these taxa are isomorphic, respectively compatible. These ..."
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Cited by 9 (4 self)
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Given a set of evolutionary trees on a same set of taxa, the maximum agreement subtree problem (MAST), respectively maximum compatible tree problem (MCT), consists of finding a largest subset of taxa such that all input trees restricted to these taxa are isomorphic, respectively compatible. These problems
Evolutionary computation: Challenges and duties
- FRONTIERS OF EVOLUTIONARY COMPUTATION
, 2004
"... Evolutionary Computation (EC) is now a few decades old. The impressive development of the field since its initial conception has made it one of the most vigorous research areas, specifically from an applied viewpoint. This should not hide the existence of some major gaps in our understanding on thes ..."
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Cited by 2 (1 self)
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Evolutionary Computation (EC) is now a few decades old. The impressive development of the field since its initial conception has made it one of the most vigorous research areas, specifically from an applied viewpoint. This should not hide the existence of some major gaps in our understanding on these techniques. In this essay we propose a number of challenging tasks that –according to our opinion – should be attacked in order to fill some of these gaps. They mainly refer to the theoretical basis of the paradigm; we believe that an effective cross-fertilization among different areas of Theoretical Computer Science and Artificial Intelligence (such as Parameterized Complexity and Modal Logic) is mandatory for developing a new corpus of knowledge about EC.
Detecting Traditional Packers, Decisively
"... Abstract. Many important decidability results in malware analysis are based on Turing machine models of computation. We exhibit computational models that use more realistic assumptions about machine and attacker resources. While seminal results such as [1–5] remain true for Turing machines, we show ..."
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Cited by 1 (0 self)
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Abstract. Many important decidability results in malware analysis are based on Turing machine models of computation. We exhibit computational models that use more realistic assumptions about machine and attacker resources. While seminal results such as [1–5] remain true for Turing machines, we show that under more realistic assumptions important tasks are decidable instead of undecidable. Specifically, we show that detecting traditional malware unpacking behavior – in which a payload is decompressed or decrypted and subsequently executed – is decidable under our assumptions. We then examine the issue of dealing with complex but decidable problems, and look for lessons from the hardware verification community, which has been striving to meet the challenge of intractable problems for the past three decades. 1
Rotation Distance is Fixed-Parameter Tractable
, 2009
"... Rotation distance between trees measures the number of simple operations it takes to transform one tree into another. There are no known polynomial-time algorithms for computing rotation distance. In the case of ordered rooted trees, we show that the rotation distance between two ordered trees is fi ..."
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Cited by 1 (0 self)
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Rotation distance between trees measures the number of simple operations it takes to transform one tree into another. There are no known polynomial-time algorithms for computing rotation distance. In the case of ordered rooted trees, we show that the rotation distance between two ordered trees is fixed-parameter tractable, in the parameter, k, the rotation distance. The proof relies on the kernalization of the initial trees to trees with size bounded by 7k. 1
Computational techniques to enable visualizing shapes of objects of extra spatial dimensions
, 2010
"... ..."
Solving Minimum Vertex Cover: A Fast Fixed-Parameter-Tractable Algorithm for Profit Cover
, 2002
"... We introduce the problem Profit Cover which is an adaptation of the graph problem Vertex Cover. Profit Cover finds application in the psychology of decision-making. A common assumption is that net value is a major determinant of human choice. Profit Cover incorporates the notion of net value in its ..."
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We introduce the problem Profit Cover which is an adaptation of the graph problem Vertex Cover. Profit Cover finds application in the psychology of decision-making. A common assumption is that net value is a major determinant of human choice. Profit Cover incorporates the notion of net value in its definition. For a given graph G = (V, E) and an integer p > 0, the goal is to determine a profit cover PC V such that the profit, jE j jP Cj, is at least p, where E E with (u; v) 2 E if (1) (u; v) 2 E and (2) u 2 PC or v 2 PC. We show how to use the optimization version of Profit Cover to solve Minimum Vertex Cover. In addition to the classical complexity we of this profit problem, we consider its the complexity of its natural parameterization on profit p, p-Profit Cover. We show that Profit Cover is NP-complete and present a fixed-parameter-tractable algorithm for p-Profit Cover that has a time-complexity of O(pjV j + 1:236506 ). The algorithm is a combination of kernelizing the graph to a linear size in p, a bounded-search-tree algorithm and re-kernelization. The same techniques also yield a fixed-parameter-tractable algorithm of the same time complexity solving the more general problem p-Edge Weighted Profit Cover, where each edge e 2 E is associated a weight, that is a positive integer w(e) > 0, and the profit is determined by e2E 0 w(e) jP Cj.
