A Constructive linear time algorithm for small cutwidth

The cutwidth of a graph G is defined to be the smallest integer k such that the vertices of G can be arranged in a linear layout [v(1),...,v(n)] in such a way that for every i=1,...,n-1, there are at most k edges with the one endpoint in {v(1),...,v(i)} and the other in {v(i+1),...,v(n)}. In this paper we show how to construct, for any constant k, a linear time algorithm that for any input graph G, answers whether G has cutwidth at most k and, in the case of a positive answer, outputs the corresponding linear layout.

[1]  Dimitrios M. Thilikos,et al.  Constructive Linear Time Algorithms for Branchwidth , 1997, ICALP.

[2]  Michael R. Fellows,et al.  On Well-Partial-Order Theory and its Application to Combinatorial Problems of VLSI Design , 1989, SIAM J. Discret. Math..

[3]  Paul D. Seymour,et al.  Graphs with small bandwidth and cutwidth , 1989, Discret. Math..

[4]  Ephraim Korach,et al.  Tree-Width, Path-Widt, and Cutwidth , 1993, Discret. Appl. Math..

[5]  Fan Chung,et al.  ON THE CUTWIDTH AND THE TOPOLOGICAL BANDWIDTH OF A TREE , 1985 .

[6]  Michael R. Fellows,et al.  On search decision and the efficiency of polynomial-time algorithms , 1989, STOC '89.

[7]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[8]  Hans L. Bodlaender.  A linear time algorithm for finding tree-decompositions of small treewidth , 1993, STOC '93.

[9]  Mihalis Yannakakis,et al.  A polynomial algorithm for the MIN CUT linear arrangement of trees , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[10]  Neil Robertson,et al.  Graph Minors .XIII. The Disjoint Paths Problem , 1995, J. Comb. Theory B.

[11]  Fillia Makedon,et al.  On minimizing width in linear layouts , 1989, Discret. Appl. Math..

[12]  Ivan Hal Sudborough,et al.  Min Cut is NP-Complete for Edge Weigthed Trees , 1986, ICALP.

[13]  Michael R. Fellows,et al.  Finite automata, bounded treewidth, and well-quasiordering , 1991, Graph Structure Theory.

[14]  Joseph Naor,et al.  Divide-and-conquer approximation algorithms via spreading metrics , 2000, JACM.

[15]  Ton Kloks,et al.  Efficient and Constructive Algorithms for the Pathwidth and Treewidth of Graphs , 1993, J. Algorithms.

[16]  Michael R. Fellows,et al.  On search, decision, and the efficiency of polynomial-time algorithms , 1994, FOCS 1994.

[17]  Hans L. Bodlaender.  Improved Self-reduction Algorithms for Graphs with Bounded Treewidth , 1994, Discret. Appl. Math..

[18]  Hans L. Bodlaender,et al.  A linear time algorithm for finding tree-decompositions of small treewidth , 1993, STOC.

[19]  Fillia Makedon,et al.  Topological Bandwidth , 1983, CAAP.