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761
On Parse Trees and MyhillNerodetype Tools for handling Graphs of Bounded Rankwidth
, 2008
"... Rankwidth is a structural graph measure introduced by Oum and Seymour and aimed at better handling of graphs of bounded cliquewidth. We propose a formal framework and tools for easy design of dynamic algorithms running directly on a rankdecomposition of a graph (on contrary to the usual approach ..."
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Cited by 19 (7 self)
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Rankwidth is a structural graph measure introduced by Oum and Seymour and aimed at better handling of graphs of bounded cliquewidth. We propose a formal framework and tools for easy design of dynamic algorithms running directly on a rankdecomposition of a graph (on contrary to the usual
Automata Approach to Graphs of Bounded Rankwidth
"... Abstract. Rankwidth is a rather new structural graph measure introduced by Oum and Seymour in 2003 in order to find an efficiently computable approximation of cliquewidth of a graph. Being a very nice graph measure indeed, the only serious drawback of rankwidth was that it is virtually impossibl ..."
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Cited by 4 (2 self)
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decompositions of Courcelle and Kante ́ [WG’07]. We then use our labeling parse trees to build a MyhillNerodetype formalism for handling restricted classes of graphs of bounded rankwidth, and to directly prove that (an already indirectly known result) all graph properties expressible in MSO logic are decidable by finite
Better polynomial algorithms on graphs of bounded rankwidth
 In IWOCA’09, LNCS
, 2009
"... Abstract. Although there exist many polynomial algorithms for NPhard problems running on a cliquewidth expression of the input graph, there exists only little comparable work on such algorithms for rankwidth. We believe that one reason for this is the somewhat obscure and hardtograsp nature of ..."
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Cited by 4 (1 self)
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algorithms solving hard problems (nonFPT) on graphs of bounded rankwidth. Those include computing the chromatic number and polynomial or testing the Hamiltonicity of a graph and are extendable to many other problems.
Constraint Logic Programming: A Survey
"... Constraint Logic Programming (CLP) is a merger of two declarative paradigms: constraint solving and logic programming. Although a relatively new field, CLP has progressed in several quite different directions. In particular, the early fundamental concepts have been adapted to better serve in differe ..."
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Cited by 864 (25 self)
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Constraint Logic Programming (CLP) is a merger of two declarative paradigms: constraint solving and logic programming. Although a relatively new field, CLP has progressed in several quite different directions. In particular, the early fundamental concepts have been adapted to better serve in different areas of applications. In this survey of CLP, a primary goal is to give a systematic description of the major trends in terms of common fundamental concepts. The three main parts cover the theory, implementation issues, and programming for applications.
MyhillNerode methods for hypergraphs
 IN PROC. OF ISAAC 2013, LNCS
, 2013
"... We introduce a method of applying MyhillNerode methods from formal language theory to hypergraphs and show how this method can be used to obtain the following parameterized complexity results. – Hypergraph Cutwidth (deciding whether a hypergraph on n vertices has cutwidth at most k) is lineartime ..."
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Cited by 2 (1 self)
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time solvable for constant k. – For hypergraphs of constant incidence treewidth (treewidth of the incidence graph), Hypertree Width and variants cannot be solved by simple finite tree automata. The proof leads us to conjecture that Hypertree Width is W[1]hard for this parameter.
Unified Approach to Polynomial Algorithms on Graphs of Bounded (bi)Rankwidth
, 2009
"... In this paper we develop new algorithmic machinery for solving hard problems on graphs of bounded rankwidth and on digraphs of bounded birankwidth in polynomial (XP, to be precise) time. These include, particularly, graph colouring and chromatic polynomial problems, the Hamiltonian path and cmi ..."
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Cited by 5 (2 self)
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In this paper we develop new algorithmic machinery for solving hard problems on graphs of bounded rankwidth and on digraphs of bounded birankwidth in polynomial (XP, to be precise) time. These include, particularly, graph colouring and chromatic polynomial problems, the Hamiltonian path and c
Branchwidth, parse trees, and monadic secondorder logic for matroids
, 2005
"... We introduce “matroid parse trees” which, using only a limited amount of information at each node, can build up the vector representations of matroids of bounded branchwidth over a finite field. We prove that if M is a family of matroids described by a sentence in the monadic secondorder logic of ..."
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” for graphs of bounded treewidth by Courcelle, and others. Moreover, applications and relations in areas other than matroid theory can be found, like for rankwidth of graphs, or in the coding theory.
New Width Parameters of Graphs
, 2012
"... The main focus of this thesis is on using the divide and conquer technique to efficiently solve graph problems that are in general intractable. We work in the field of parameterized algorithms, using width parameters of graphs that indicate the complexity inherent in the structure of the input graph ..."
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Cited by 6 (2 self)
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parameters by defining partial orders of width parameters. We focus on treewidth, branchwidth, cliquewidth, modulewidth and rankwidth, and include a Hasse diagram of these orders containing 32 graph parameters. We use the size of a maximum matching in a bipartite graph as a set function to define MMwidth
Exploiting Parse Trees for Graphs of Bounded Treewidth
"... This thesis studies a structural framework for representing graphs of bounded treewidth, called a [treewidth] tparse. This is a natural extension of the Cattell–Dinneen [pathwidth] tparses, which they used in their platform for finding forbidden minors. Our tparses are quite useful for representi ..."
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for representing graphs (in parsed form) for the many dynamic programs that are available for graphs of bounded treewidth. To highlight our theoretical model, we have implemented a concrete lineartime application (a treeautomaton based algorithm) for the VERTEX COVER problem for input graphs in tparse form
Implementing Mathematics with The Nuprl Proof Development System
, 1986
"... Problem solving is a significant part of science and mathematics and is the most intellectually significant part of programming. Solving a problem involves understanding the problem, analyzing it, exploring possible solutions, writing notes about intermediate results, reading about relevant methods, ..."
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Cited by 190 (18 self)
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Problem solving is a significant part of science and mathematics and is the most intellectually significant part of programming. Solving a problem involves understanding the problem, analyzing it, exploring possible solutions, writing notes about intermediate results, reading about relevant methods, checking results, and eventually assembling a solution. Nuprl is a computer system which provides assistance with this activity. It supports the interactive creation of proofs, formulas, and terms in a formal theory of mathematics
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