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34
Modular Decomposition and Transitive Orientation
, 1999
"... A module of an undirected graph is a set X of nodes such for each node x not in X, either every member of X is adjacent to x, or no member of X is adjacent to x. There is a canonical linearspace representation for the modules of a graph, called the modular decomposition. Closely related to modular ..."
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Cited by 90 (14 self)
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A module of an undirected graph is a set X of nodes such for each node x not in X, either every member of X is adjacent to x, or no member of X is adjacent to x. There is a canonical linearspace representation for the modules of a graph, called the modular decomposition. Closely related to modular decomposition is the transitive orientation problem, which is the problem of assigning a direction to each edge of a graph so that the resulting digraph is transitive. A graph is a comparability graph if such an assignment is possible. We give O(n +m) algorithms for modular decomposition and transitive orientation, where n and m are the number of vertices and edges of the graph. This gives linear time bounds for recognizing permutation graphs, maximum clique and minimum vertex coloring on comparability graphs, and other combinatorial problems on comparability graphs and their complements.
Performance and Reliability Analysis Using Directed Acyclic Graphs
 IEEE Trans. Software Eng
, 1987
"... AbstractA graphbased modeling technique has been developed for the stochastic analysis of systems containing concurrency. The basis of the technique is the use of directed acyclic graphs. These graphs represent eventprecedence networks where activities may occur serially, probabilistically, or co ..."
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Cited by 39 (5 self)
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AbstractA graphbased modeling technique has been developed for the stochastic analysis of systems containing concurrency. The basis of the technique is the use of directed acyclic graphs. These graphs represent eventprecedence networks where activities may occur serially, probabilistically, or concurrently. When a set of activities occurs concurrently, the condition for the set of activities to complete is that a specified number of the activities must complete. This includes the special cases that one or all of the activities must complete. The cumulative distribution function associated with an activity is assumed to have exponential polynomial form. Further generality is obtained by allowing these distributions to have a mass at the origin and/or at infinity. The distribution function for the time taken to complete the entire graph is computed symbolically in the time parameter t. The technique allows two or more graphs to be combined hierarchically. Applications of the technique to the evaluation of concurrent program execution time and to the reliability analysis of faulttolerant systems are discussed. Index TermsAvailability, directed acyclic graphs, faulttolerance, Markov models, performance evaluation, program performance, reliability. I.
Pomset Logic: A NonCommutative Extension of Classical Linear Logic
, 1997
"... We extend the multiplicative fragment of linear logic with a noncommutative connective (called before), which, roughly speaking, corresponds to sequential composition. This lead us to a calculus where the conclusion of a proof is a Partially Ordered MultiSET of formulae. We firstly examine coherenc ..."
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Cited by 37 (8 self)
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We extend the multiplicative fragment of linear logic with a noncommutative connective (called before), which, roughly speaking, corresponds to sequential composition. This lead us to a calculus where the conclusion of a proof is a Partially Ordered MultiSET of formulae. We firstly examine coherence semantics, where we introduce the before connective, and ordered products of formulae. Secondly we extend the syntax of multiplicative proof nets to these new operations. We then prove strong normalisation, and confluence. Coming back to the denotational semantics that we started with, we establish in an unusual way the soundness of this calculus with respect to the semantics. The converse, i.e. a kind of completeness result, is simply stated: we refer to a report for its lengthy proof. We conclude by mentioning more results, including a sequent calculus which is interpreted by both the semantics and the proof net syntax, although we are not sure that it takes all proof nets into account...
Efficient and practical algorithms for sequential modular decomposition
, 1999
"... A module of an undirected graph G = (V, E) is a set X of vertices that have the same set of neighbors in V \ X. The modular decomposition is a unique decomposition of the vertices into nested modules. We give a practical algorithm with an O(n + m(m;n)) time bound and a variant with a linear time bou ..."
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Cited by 30 (1 self)
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A module of an undirected graph G = (V, E) is a set X of vertices that have the same set of neighbors in V \ X. The modular decomposition is a unique decomposition of the vertices into nested modules. We give a practical algorithm with an O(n + m(m;n)) time bound and a variant with a linear time bound.
Perfect Dominating Sets
, 1990
"... A dominating set S of a graph G is perfect if each vertex of G is dominated by exactly one vertex in S. We study the existence and construction of PDSs in families of graphs arising from the interconnection networks of parallel computers. These include trees, dags, seriesparallel graphs, meshes, to ..."
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Cited by 18 (2 self)
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A dominating set S of a graph G is perfect if each vertex of G is dominated by exactly one vertex in S. We study the existence and construction of PDSs in families of graphs arising from the interconnection networks of parallel computers. These include trees, dags, seriesparallel graphs, meshes, tori, hypercubes, cubeconnected cycles, cubeconnected paths, and de Bruijn graphs. For trees, dags, and seriesparallel graphs we give linear time algorithms that determine if a PDS exists, and generate a PDS when one does. For 2 and 3dimensional meshes, 2dimensional tori, hypercubes, and cubeconnected paths we completely characterize which graphs have a PDS, and the structure of all PDSs. For higher dimensional meshes and tori, cubeconnected cycles, and de Bruijn graphs, we show the existence of a PDS in infinitely many cases, but our characterization is not complete. Our results include distance ddomination for arbitrary d. 1 Introduction Suppose G = (V; E) is a graph with vertex se...
Pomset Logic as an Alternative Categorial Grammar
 IN FORMAL GRAMMAR
, 1995
"... Lambek calculus may be viewed as a fragment of linear logic, namely intuitionistic noncommutative multiplicative linear logic. As it is too restrictive to describe numerous usual linguistic phenomena, instead of extending it we extend MLL with a noncommutative connective, thus dealing with partia ..."
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Cited by 17 (2 self)
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Lambek calculus may be viewed as a fragment of linear logic, namely intuitionistic noncommutative multiplicative linear logic. As it is too restrictive to describe numerous usual linguistic phenomena, instead of extending it we extend MLL with a noncommutative connective, thus dealing with partially ordered multisets of formulae. Relying on proof net technique, our study associates words with parts of proofs, modules, and parsing is described as proving by plugging modules. Apart from avoiding spurious ambiguities, our method succeeds in obtaining a logical description of relatively free word order, headwrapping, clitics, and extraposition (these latest two constructions are unfortunately not included, for lack of space).
A Computational Study on Bounding the Makespan Distribution in Stochastic Project Networks
 ANNALS OF OPERATIONS RESEARCH
, 1998
"... Given a stochastic project network with independently distributed activity durations, several approaches to bound the distribution function of the project completion time have been proposed. We have implemented the most promising of these algorithms and compare their behavior on a basis of nearly 20 ..."
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Cited by 14 (1 self)
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Given a stochastic project network with independently distributed activity durations, several approaches to bound the distribution function of the project completion time have been proposed. We have implemented the most promising of these algorithms and compare their behavior on a basis of nearly 2000 instances with up to 1200 activities of different testbeds. We propose a suitable numerical representation of the given distributions which is the basis for excellent computational results.
Rationality in Algebras With a Series Operation
 Information and Computation
, 2000
"... . This paper considers languages in a free algebra which has a binary associative operation called the series product. We define automata operating in these algebras and rational expressions, and we show that their expressive powers coincide (a Kleene theorem). We also show that this expressive p ..."
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Cited by 14 (4 self)
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. This paper considers languages in a free algebra which has a binary associative operation called the series product. We define automata operating in these algebras and rational expressions, and we show that their expressive powers coincide (a Kleene theorem). We also show that this expressive power equals that of algebraic recognizability (a MyhillNerode theorem). This generalizes the work of Thatcher and Wright. The first equivalence continues to hold when conditions such as associativity and commutativity are imposed on the term operations, but recognizability is weaker when one of the term operations (other than the series product) is associative. We also consider languages which have a bound on the number of nested occurrences of certain designated term operations and get both the equivalences mentioned above. This generalizes our earlier work and answers a question left open therein. 1 Automata form one of the most commonly used computing device, from their histor...
A Complete Axiomatisation for the Inclusion of SeriesParallel Partial Orders
, 1997
"... Seriesparallel orders are defined as the least class of partial orders containing the oneelement order and closed by ordinal sum and disjoint union. From this inductive denition, it is almost immediate that any seriesparallel order may be represented by an algebraic expression, which is unique up ..."
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Cited by 13 (6 self)
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Seriesparallel orders are defined as the least class of partial orders containing the oneelement order and closed by ordinal sum and disjoint union. From this inductive denition, it is almost immediate that any seriesparallel order may be represented by an algebraic expression, which is unique up to the associativivity of ordinal sum and to the associativivity and commutativity of disjoint union. In this paper, we introduce a rewrite system acting on these algebraic expressions that axiomatises completely the subordering relation for the class of seriesparallel orders.