S. Arnborg. Efficient algorithms for combinatorial problems on graphs with bounded decomposability -- A survey. BIT, 25:2--23, 1985. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
First 50 documents Next 50
Treewidth and Small Separators for Graphs with Small Chordality - Bodlaender, Thilikos (1995) (Correct)
....decomposed into a tree structure of pieces with at most k 1 vertices. For the precise definition, see Section 2. A series of recent results show that many NP complete problems become polynomial or even linear time solvable, or belong to NC, when restricted to graphs with small treewidth (see [5, 7, 9]) Much research has been done on the problem of determining the treewidth and the pathwidth of a graph, and finding optimal tree or path decompositions with optimal treewidth or pathwidth. These problems are NP complete even if we restrict the input graph on cocomparability graphs [23] bipartite ....
....Theorem 1 For any fixed integer k, there is a linear time algorithm, that tests whether a given graph G = V; E) has treewidth at most k, and if so, outputs a tree decomposition of G with treewidth at most k. Treewidth can be characterized in terms of elimination orderings. Arnborg introduced in [5] the notion of the elimination dimension of a graph and proved that it is equivalent with treewidth. We give the definition of the s elimination dimension of a graph introduced in [19] For the case where s = n Gamma 1, this parameter is equivalent to treewidth. An elimination ordering of a ....
[Article contains additional citation context not shown here]
S. Arnborg, "Efficient algorithms for combinatorial problems on graphs with bounded decomposability (A survey)", BIT, 25 (1985), 2--33.
The Hardness of Problems on Thin Colored Graphs - Bodlaender, Fellows.. (1995) (Correct)
....of Bodlaender [6] we can determine that no such decomposition of width b(k) exists or be given a decomposition of G. In either case, the running time for this procedure is linear in the size of G but exponential only in k. By means of one of several general algorithmic design methodologies (see [1, 4, 5, 15, 20, 54]) we may then answer the original question in time linear in the size of G. Hence, for small values of k, this procedure may lead to algorithms that are practical even for very large graphs G. Examples where these methods have been successful include Treewidth, Pathwidth, Min Cut Linear ....
S. Arnborg. Efficient algorithms for combinatorial problems on graphs with bounded decomposability: a survey. BIT, 25:2--23, 1985.
The Pathwidth and Treewidth of Cographs - Bodlaender, Möhring (1990) (35 citations) (Correct)
....Report RUU CS 90 7 Utrecht University P.O. Box 80.089 3508 TB Utrecht The Netherlands 0924 ] 275 I Introduction The pathwidth and treewidth of a graph are two notions with a large number of different applications in many areas, like algorithmic graph theory, VLSI design and others (see e.g. [1, 13]) Unfortunately, determining the pathwidth or treewidth of a given graph is NP complete [2] In this paper we show that there are efficient algorithms for determining the pathwidth or treewidth of a cograph. We also derive some technical lemmas, which are not only necessary to prove correctness ....
.... problem of determining whether the pathwidth or treewidth of a given graph is at most k can be solved in polynomial time with dynamic programming [2, 8] and in O(n 2) time with graph minor theory [5, 16] The notions of pathwidth and treewidth have several equivalent characterizations (see e.g. [1, 13, 18]. For instance, a graph is a partial k tree, if and only if its treewidth is at most k. This paper is further organized as follows. In section 2 we give most necessary definitions and some preliminary results. In section 3 we prove a number of interesting graph theoretic lemmas and theorems. In ....
[Article contains additional citation context not shown here]
S. Arnborg. Efficient algorithms for combinatorial problems on graphs with bounded decomposability- A Survey. BIT, 25:2-23, 1985.
Computing the Treewidth and the Minimum Fill-in With the.. - Bodlaender, Rotics (2001) (Correct)
....to find treewidth(G) for a given graph G. The MINIMUM FILL IN problem is to find rain fill in(G) for a given graph G. These problems have drawn much attention due to applications in areas such as Gaussian elimination of matrix, VLSI layout, gate matrix layout and algorithmic graph theory (see e.g. [1, 5, 24]) Both problems are NP hard in general [2, 27] but polynomial time algorithms exists for many special graph classes such as: permutation graphs [6] circular arc graphs [26] circle graphs [19] distance hereditary graphs [12] q,q 4) graphs [3] and HHDfree graphs [11] Bouchitt and Todinca [8, ....
S. Arnborg. Efficient algorithms for combinatorial problems on graphs with bounded decomposability A survey. BIT, 25:2 23, 1985.
On the Treewidth and Pathwidth of Permutation Graphs - Kloks, al. (1992) (22 citations) (Correct)
.... graphs with treewidth at most k is exactly the class of partial k trees (see e.g. 21] 16] There exist linear time algorithms for many NP complete problems, when restricted to the class of partial k trees for some constant k and when a tree decomposition with bounded width is given (see e.g. [1], 5] 7] 3] and [21] Determining whether the treewidth or pathwidth of a given graph is at most a given integer k is NP complete ( 2] In view of this the results of Robertson and Seymour on minor closed classes of graph are of great interest. Definition 2.6 An elementary contraction of a ....
S. Arnborg, Efficient algorithms for combinatorial problems on graphs with bounded decomposability -- A survey. BIT, 25, 2 - 23, 1985.
Easy Problems for Tree-Decomposable Graphs - Arnborg, Lagergren (1991) (141 citations) Self-citation (Arnborg) (Correct)
.... Present address: FB 11 Computer Science, Univerity Dulsburg, Pf 10 15 03, C W 4100, Dulsburg 1, Germany. 3O8 0196 6774 91 3.00 Copyright 1991 by Academic Press, Inc. All rights of reproduction in any form reserved. as far back as the middle of the nineteenth century (for a survey see [3]) and there are clear analogies with the theory of non serial dynamic programming as described by Bertele and Brioschi [9] the systematic study of this problem had of course to await the recognition of the NP complete ness concept. This research area started in the 1970s with a large number ....
....of treewidth as a decomposition tool, and a similar coding as in Section 4 takes us to binary trees. It is also possible to interpret graphs of bounded treewidth into trees obtained from parse trees of the given graphs, as defined in [15, 19, 43] Co graphs [18] and complement k decomposable [3] graphs can be interpreted into binary trees, but in these cases it is not possible to allow edge sets or evaluations on edges in the MS formulae (and thus the incidence relations are only indirectly accessible via the (directed or undirected) adjacency relation) So we have shown in the examples ....
S. ARNBORG, Efficient algorithms for combinatorial problems on graphs with bounded decomposability--A survey, BIT 25 (1985), 2-33.
Constructive Linear Time Algorithms For - Branchwidth Dimitrios Thilikos (2000) (Correct)
No context found.
S. Arnborg. Efficient algorithms for combinatorial problems on graphs with bounded decomposability -- A survey. BIT, 25:2--23, 1985.
Exact, Upper, and Lower Bounds on - Treewidth Emgad Bachoore (2006) (Correct)
No context found.
S. Arnborg. Efficient algorithms for combinatorial problems on graphs with bounded decomposability - A survey. BIT, 8:277-284, 1987.
AND/OR Tree Search for Constraint Optimization - Radu Marinescu And (Correct)
No context found.
Arnborg, S. A. 1985. Efficient algorithms for combinatorial problems on graphs with bounded decomposability. BIT 25:2--23.
A Scheme for Approximating Probabilistic Inference - Rina Dechter And (1997) (15 citations) (Correct)
No context found.
S. A. Arnborg. Efficient algorithms for combinatorial problems on graphs with bounded decomposability - a survey. BIT, 25:2--23, 1985.
Bucket Elimination: A Unifying Framework for Probabilistic.. - Dechter (1996) (74 citations) (Correct)
No context found.
S. Arnborg, "Efficient algorithms for combinatorial problems on graphs with bounded decomposability - A survey" Bit 25 (1985):2-23.
The Impact of AND/OR Search Spaces on Constraint.. - Dechter, Mateescu (2004) (Correct)
No context found.
Arnborg, S.A.: Efficient algorithms for combinatorial problems on graphs with bounded decomposability - a survey. BIT 25 (1985) 2--23
Mini-Buckets: A General Scheme for Generating Approximations in.. - Dechter (1997) (10 citations) (Correct)
No context found.
S. A. Arnborg. Efficient algorithms for combinatorial problems on graphs with bounded decomposability - a survey. BIT, 25:2--23, 1985.
A General Scheme for Multiple Lower Bound - Computation In Constraint (Correct)
No context found.
S.A. Arnborg. Efficient algorithms for combinatorial problems on graphs with bounded decomposability - a survey. BIT, 25:2--23, 1985.
Computational Experiments on Graph Width Metrics - Fouhy (2003) (1 citation) (Correct)
No context found.
ARNBORG, S. Efficient algorithms for combinatorial problems on graphs with bounded decomposability (a survey). BIT, 25 (1985), 2-- 33.
Fixed-Parameter Tractability and Completeness I: Basic Results - Downey, Fellows (1995) (145 citations) (Correct)
No context found.
S. Arnborg, "Efficient Algorithms for Combinatorial Problems on Graphs with Bounded Decomposability --- A Survey," BIT 25 (1985), 2-23.
Iterative Algorithms for Graphical Models - Mateescu (2003) (Correct)
No context found.
Arnborg, S. A. 1985. Efficient algorithms for combinatorial problems on graphs with bounded decomposability - a survey. BIT 25:2--23.
AND/OR Search Spaces for Graphical Models - Rina Dechter Department (2004) (3 citations) (Correct)
No context found.
Arnborg, S. A. 1985. Efficient algorithms for combinatorial problems on graphs with bounded decomposability - a survey. BIT 25:2--23.
On Finding Minimal W-Cutset Problem - Bozhena Bidyuk And (Correct)
No context found.
S. A. Arnborg, `Efficient algorithms for combinatorial problems on graphs with bounded decomposability - a survey', BIT, 25, 2--23, (1985).
Guiding SAT Diagnosis with Tree Decompositions - Bjesse, Kukula, Damiano.. (2004) (1 citation) (Correct)
No context found.
S. Arnborg. Efficient Algorithms for Combinatorial Problems on Graphs with Bounded Decomposability - A Survey. BIT, 25:2--23, 1985.
Mini-Buckets: A General Scheme for Approximating Inference - Dechter, Rish (1998) (4 citations) (Correct)
No context found.
S.A. Arnborg. Efficient algorithms for combinatorial problems on graphs with bounded decomposability - a survey. BIT, 25:2--23, 1985.
Models and Approximation Algorithms for Channel Assignment .. - Krumke, Marathe, Ravi (2000) (7 citations) (Correct)
No context found.
S. Arnborg, Efficient Algorithms for Combinatorial Problems on Graphs with Bounded Decomposability, BIT, 25 (1985), pp. 2--23.
NC-Algorithms for Graphs with Small Treewidth - Bodlaender (1988) (14 citations) (Correct)
No context found.
S. Arnborg. Efficient algorithms for combinatorial problems on graphs with bounded decomposability - A survey. BIT, 25:2-23, 1985.
Treewidth and Pathwidth of Permutation Graphs - Bodlaender, Kloks, Kratsch (1992) (22 citations) (Correct)
No context found.
S. Arnborg, Efficient algorithms for combinatorial problems on graphs with bounded decomposability -- A survey. BIT 25, 2 - 23, 1985.
On Linear Time Minor Tests And Depth First Search - Bodlaender (1989) (8 citations) (Correct)
No context found.
S. Arnborg. Efficient algorithms for combinatorial problems on graphs with bounded decomposability- A survey. BIT, 25:2-23, 1985.
First 50 documents Next 50
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC