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Algebraic recognizability of languages
 In Proc. 29th Int. Symp. Math. Found. of Comp. Sci. (MFCS’04
, 2004
"... Abstract. Recognizable languages of finite words are part of every computer science cursus, and they are routinely described as a cornerstone for applications and for theory. We would like to briefly explore why that is, and how this wordrelated notion extends to more complex models, such as those ..."
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Cited by 11 (3 self)
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Abstract. Recognizable languages of finite words are part of every computer science cursus, and they are routinely described as a cornerstone for applications and for theory. We would like to briefly explore why that is, and how this wordrelated notion extends to more complex models, such as those developed for modeling distributed or timed behaviors. In the beginning was the Word... Recognizable languages of finite words are part of every computer science cursus, and they are routinely described as a cornerstone for applications and for theory. We would like to briefly explore why that is, and how this wordrelated notion extends to more complex models, such as those developed for modeling distributed or timed behaviors. The notion of recognizable languages is a familiar one, associated with classical theorems by Kleene, Myhill, Nerode, Elgot, Büchi, Schützenberger, etc. It can be approached from several angles: recognizability by automata, recognizability by finite monoids or finiteindex congruences, rational expressions, monadic second
Structure and Stability Number of Chair, CoP and GemFree Graphs Revisited
, 2002
"... The P 4 is the induced path with vertices a; b; c; d and edges ab; bc; cd. The chair (coP, gem) has a fifth vertex adjacent to b (a and b, a; b; c and d respectively). We give a complete structure description of prime chair, coP and gemfree graphs which implies bounded clique width for this gra ..."
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Cited by 10 (3 self)
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The P 4 is the induced path with vertices a; b; c; d and edges ab; bc; cd. The chair (coP, gem) has a fifth vertex adjacent to b (a and b, a; b; c and d respectively). We give a complete structure description of prime chair, coP and gemfree graphs which implies bounded clique width for this graph class. It is known that this has some nice consequences; very roughly speaking, every problem expressible in a certain kind of Monadic Second Order Logic (quantifying only over vertex set predicates) can be solved efficiently for graphs of bounded clique width. In particular, we obtain linear time for the problems Vertex Cover, Maximum Weight Stable Set (MWS), Maximum Weight Clique, Steiner Tree, Domination and Maximum Induced Matching on chair, coP and gemfree graphs and a slightly larger class of graphs. This drastically improves a recently published O(n ) time bound for Maximum Stable Set on buttery, chair, coP and gemfree graphs.
Ordered Vertex Partitioning
, 2000
"... A transitive orientation of a graph is an orientation of the edges that produces a transitive digraph. The modulardecomposition of a graph is a canonical representation of all of its modules. Finding a transitive orientation and finding the modular decomposition are in some sense dual problems. In t ..."
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Cited by 7 (3 self)
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A transitive orientation of a graph is an orientation of the edges that produces a transitive digraph. The modulardecomposition of a graph is a canonical representation of all of its modules. Finding a transitive orientation and finding the modular decomposition are in some sense dual problems. In this paper, we describe a simple O(n+mlogn)algorithm that uses this duality to find both a transitive orientation and the modular decomposition. Though the running time is not optimal, this algorithm is much simpler than any previous algorithms that are not Ω(n²). The bestknown time bounds for the problems are O(n + m), but they involve sophisticated techniques.
Gem and CoGemFree Graphs Have Bounded CliqueWidth
, 2003
"... The P 4 is the induced path of four vertices. The gem consists of a P 4 with an additional universal vertex being completely adjacent to the P 4 , and the cogem is its complement graph. Gem and cogemfree graphs generalize the popular class of cographs (i. e. P 4 free graphs). The tree structure ..."
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Cited by 7 (5 self)
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The P 4 is the induced path of four vertices. The gem consists of a P 4 with an additional universal vertex being completely adjacent to the P 4 , and the cogem is its complement graph. Gem and cogemfree graphs generalize the popular class of cographs (i. e. P 4 free graphs). The tree structure and algebraic generation of cographs has been crucial for several concepts of graph decomposition such as modular and homogeneous decomposition. Moreover, it is fundamental for the recently introduced concept of cliquewidth of graphs which extends the famous concept of treewidth. It is wellknown that the cographs are exactly those graphs of cliquewidth at most 2.
Fully Dynamic Algorithm for Recognition and Modular Decomposition of Permutation Graphs
 ALGORITHMICA
, 2009
"... This paper considers the problem of maintaining a compact representation (O(n) space) of permutation graphs under vertex and edge modifications (insertion or deletion). That representation allows us to answer adjacency queries in O(1) time. The approach is based on a fully dynamic modular decomposit ..."
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Cited by 7 (4 self)
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This paper considers the problem of maintaining a compact representation (O(n) space) of permutation graphs under vertex and edge modifications (insertion or deletion). That representation allows us to answer adjacency queries in O(1) time. The approach is based on a fully dynamic modular decomposition algorithm for permutation graphs that works in O(n) time per edge and vertex modification. We thereby obtain a fully dynamic algorithm for the recognition of permutation graphs.
Algebraic Operations on PQ Trees and Modular Decomposition Trees
, 2005
"... Partitive set families are families of sets that can be quite large, but have a compact, recursive representation in the form of a tree. This tree is a common generalization of PQ trees, the modular decomposition of graphs, certain decompositions of boolean functions, and decompositions that arise o ..."
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Cited by 6 (1 self)
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Partitive set families are families of sets that can be quite large, but have a compact, recursive representation in the form of a tree. This tree is a common generalization of PQ trees, the modular decomposition of graphs, certain decompositions of boolean functions, and decompositions that arise on a variety of other combinatorial structures. We describe natural operators on partitive set families, give algebraic identities for manipulating them, and describe efficient algorithms for evaluating them. We use these results to obtain new time bounds for finding the common intervals of a set of permutations, finding the modular decomposition of an edgecolored graphs (also known as a twostructure), finding the PQ tree of a matrix when a consecutiveones arrangement is given, and finding the modular decomposition of a permutation graph when its permutation realizer is given.
SPLITPERFECT GRAPHS: CHARACTERIZATIONS AND ALGORITHMIC USE
, 2004
"... Two graphs G and H with the same vertex set V are P4isomorphic if every four vertices {a, b, c, d} ⊆V induce a chordless path (denoted by P4) inG if and only if they induce a P4 in H. We call a graph splitperfect if it is P4isomorphicto a split graph (i.e., a graph being partitionable into a cl ..."
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Cited by 6 (2 self)
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Two graphs G and H with the same vertex set V are P4isomorphic if every four vertices {a, b, c, d} ⊆V induce a chordless path (denoted by P4) inG if and only if they induce a P4 in H. We call a graph splitperfect if it is P4isomorphicto a split graph (i.e., a graph being partitionable into a clique and a stable set). This paper characterizes the new class of splitperfect graphs using the concepts of homogeneous sets and pconnected graphs and leads to a linear time recognition algorithm for splitperfect graphs, as well as efficient algorithms for classical optimization problems on splitperfect graphs based on the primeval decomposition of graphs. The optimization results considerably extend previous ones on smaller classes such as P4sparse graphs, P4lite graphs, P4laden graphs, and (7,3)graphs. Moreover, splitperfect graphs form a new subclass of brittle graphs containing the superbrittle graphs for which a new characterization is obtained leading to linear time recognition.
Homogeneity vs. adjacency: generalising some graph decomposition algorithms
 In 32nd International Workshop on GraphTheoretic Concepts in Computer Science (WG), volume 4271 of LNCS
, 2006
"... Abstract. In this paper, a new general decomposition theory inspired from modular graph decomposition is presented. Our main result shows that, within this general theory, most of the nice algorithmic tools developed for modular decomposition are still efficient. This theory not only unifies the usu ..."
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Cited by 6 (2 self)
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Abstract. In this paper, a new general decomposition theory inspired from modular graph decomposition is presented. Our main result shows that, within this general theory, most of the nice algorithmic tools developed for modular decomposition are still efficient. This theory not only unifies the usual modular decomposition generalisations such as modular decomposition of directed graphs and of 2structures, but also decomposition by star cutsets. 1
Optimal linear arrangement of interval graphs
 in Proceedings of the 31st International Symposium on Mathematical Foundations of Computer Science (MFCS 2006
"... Abstract. We study the optimal linear arrangement (OLA) problem on interval graphs. Several linear layout problems that are NPhard on general graphs are solvable in polynomial time on interval graphs. We prove that, quite surprisingly, optimal linear arrangement of interval graphs is NPhard. The s ..."
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Cited by 5 (2 self)
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Abstract. We study the optimal linear arrangement (OLA) problem on interval graphs. Several linear layout problems that are NPhard on general graphs are solvable in polynomial time on interval graphs. We prove that, quite surprisingly, optimal linear arrangement of interval graphs is NPhard. The same result holds for permutation graphs. We present a lower bound and a simple and fast 2approximation algorithm based on any interval model of the input graph. 1