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198
The computational structure of monotone monadic SNP and constraint satisfaction: A study through Datalog and group theory
 SIAM J. Comput
, 1998
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Treewidth: Algorithmic techniques and results
 In Mathematical foundations of computer science
, 1998
"... This paper gives an overview of several results and techniques for graphs algorithms that compute the treewidth of a graph or that solve otherwise intractable problems when restricted graphs with bounded treewidth more efficiently. Also, several results on graph minors are reviewed. ..."
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Cited by 133 (10 self)
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This paper gives an overview of several results and techniques for graphs algorithms that compute the treewidth of a graph or that solve otherwise intractable problems when restricted graphs with bounded treewidth more efficiently. Also, several results on graph minors are reviewed.
Linear time solvable optimization problems on graphs of bounded cliquewidth, Extended abstract
 Graph Theoretic Concepts in Computer Science, 24th International Workshop, WG ’98, Lecture Notes in Computer Science
, 1998
"... Abstract. Hierarchical decompositions of graphs are interesting for algorithmic purposes. There are several types of hierarchical decompositions. Tree decompositions are the best known ones. On graphs of treewidth at most k, i.e., that have tree decompositions of width at most k, where k is fixed, ..."
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Cited by 113 (20 self)
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Abstract. Hierarchical decompositions of graphs are interesting for algorithmic purposes. There are several types of hierarchical decompositions. Tree decompositions are the best known ones. On graphs of treewidth at most k, i.e., that have tree decompositions of width at most k, where k is fixed, every decision or optimization problem expressible in monadic secondorder logic has a linear algorithm. We prove that this is also the case for graphs of cliquewidth at most k, where this complexity measure is associated with hierarchical decompositions of another type, and where logical formulas are no longer allowed to use edge set quantifications. We develop applications to several classes of graphs that include cographs and are, like cographs, defined by forbidding subgraphs with “too many ” induced paths with four vertices. 1.
Two Strikes Against Perfect Phylogeny
 PROC. OF 19TH INTERNATIONAL COLLOQUIUM ON AUTOMATA LANGUAGES AND PROGRAMMING
, 1992
"... One of the major efforts in molecular biology is the computation of phylo genies for species sets. A longstanding open problem in this area is called the Perfect Phylogeny problem. For almost two decades the complexity of this problem remained open, with progress limited to polynomial time algor ..."
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Cited by 113 (27 self)
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One of the major efforts in molecular biology is the computation of phylo genies for species sets. A longstanding open problem in this area is called the Perfect Phylogeny problem. For almost two decades the complexity of this problem remained open, with progress limited to polynomial time algorithms for a few special cases, and many relaxations of the problem shown to be NPComplete. From an applications point of view, the problem is of interest both in its general forin, where the number of characters may vary, and in its fixedparameter form. The Perfect Phylogeny problem has been shown to be equivalent to the problem of triangulating colored graphs[30]. It has also been shown recently that for a given fixed number of characters the yesinstances have bounded treewidth[45], opening the possibility of applying methodologies for bounded treewidth to the fixedparameter form of the problem. We show that the Perfect Phylogeny problem is difficult in two different ways. We show
NCApproximation Schemes for NP and PSPACEHard Problems for Geometric Graphs
, 1997
"... We present NC approximation schemes for a number of graph problems when restricted to geometric graphs including unit disk graphs and graphs drawn in a civilized manner. Our approximation schemes exhibit the same time versus performance tradeoff as the best known approximation schemes for planar gr ..."
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Cited by 93 (1 self)
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We present NC approximation schemes for a number of graph problems when restricted to geometric graphs including unit disk graphs and graphs drawn in a civilized manner. Our approximation schemes exhibit the same time versus performance tradeoff as the best known approximation schemes for planar graphs. We also define the concept of precision unit disk graphs and show that for such graphs the approximation schemes have a better time versus performance tradeoff than the approximation schemes for arbitrary unit disk graphs. Moreover, compared to unit disk graphs, we show that for precision unit disk graphs, many more graph problems have efficient approximation schemes. Our NC approximation schemes can also be extended to obtain efficient NC approximation schemes for several PSPACEhard problems on unit disk graphs specified using a restricted version of the hierarchical specification language of Bentley, Ottmann and Widmayer. The approximation schemes for hierarchically specified un...
Query Evaluation via TreeDecompositions
 JOURNAL OF THE ACM
, 2001
"... A number of efficient methods for evaluating firstorder and monadicsecond order queries on finite relational structures are based on treedecompositions of structures or queries. We systematically study these methods. In the first part of the paper we consider arbitrary formulas on treelike struc ..."
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Cited by 83 (15 self)
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A number of efficient methods for evaluating firstorder and monadicsecond order queries on finite relational structures are based on treedecompositions of structures or queries. We systematically study these methods. In the first part of the paper we consider arbitrary formulas on treelike structures. We generalize a theorem of Courcelle [8] by showing that on structures of bounded treewidth a monadic secondorder formula (with free first and secondorder variables) can be evaluated in time linear in the structure size plus the size of the output. In the second part we study treelike formulas on arbitrary structures. We generalize the notions of acyclicity and bounded treewidth from conjunctive queries to arbitrary firstorder formulas in a straightforward way and analyze the complexity of evaluating formulas of these fragments. Moreover, we show that the acyclic and bounded treewidth fragments have the same expressive power as the wellknown guarded fragment and the finitevariable fragments of firstorder logic, respectively.
Monadic second–order evaluations on treedecomposable graphs
 Theoret. Comput. Sci
, 1993
"... Courcelle, B. and M. Mosbah, Monadic secondorder evaluations on treedecomposable graphs, ..."
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Cited by 80 (23 self)
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Courcelle, B. and M. Mosbah, Monadic secondorder evaluations on treedecomposable graphs,
A Sufficiently Fast Algorithm for Finding Close to Optimal Junction Trees
, 1996
"... An algorithm is developed for finding a close to optimal junction tree of a given graph G. ..."
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Cited by 76 (3 self)
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An algorithm is developed for finding a close to optimal junction tree of a given graph G.
Bicriteria network design problems
 In Proc. 22nd Int. Colloquium on Automata, Languages and Programming
, 1995
"... We study a general class of bicriteria network design problems. A generic problem in this class is as follows: Given an undirected graph and two minimization objectives (under different cost functions), with a budget specified on the first, find a ¡subgraph from a given subgraphclass that minimizes ..."
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Cited by 76 (13 self)
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We study a general class of bicriteria network design problems. A generic problem in this class is as follows: Given an undirected graph and two minimization objectives (under different cost functions), with a budget specified on the first, find a ¡subgraph from a given subgraphclass that minimizes the second objective subject to the budget on the first. We consider three different criteria the total edge cost, the diameter and the maximum degree of the network. Here, we present the first polynomialtime approximation algorithms for a large class of bicriteria network design problems for the above mentioned criteria. The following general types of results are presented. First, we develop a framework for bicriteria problems and their approximations. Second, when the two criteria are the same we present a “black box ” parametric search technique. This black box takes in as input an (approximation) algorithm for the unicriterion situation and generates an approximation algorithm for the bicriteria case with only a constant factor loss in the performance guarantee. Third, when the two criteria are the diameter and the total edge costs we use a clusterbased approach to devise a approximation algorithms — the solutions output violate