Τίτλος:
Cutwidth: Obstructions and Algorithmic Aspects
Γλώσσες Τεκμηρίου:
Αγγλικά
Περίληψη:
Cutwidth is one of the classic layout parameters for graphs. It measures how well one can order the vertices of a graph in a linear manner, so that the maximum number of edges between any prefix and its complement suffix is minimized. As graphs of cutwidth at most k are closed under taking immersions, the results of Robertson and Seymour imply that there is a finite list of minimal immersion obstructions for admitting a cut layout of width at most k. We prove that every minimal immersion obstruction for cutwidth at most k has size at most 2O(k3logk). As an interesting algorithmic byproduct, we design a new fixed-parameter algorithm for computing the cutwidth of a graph that runs in time 2O(k2logk)·n, where k is the optimum width and n is the number of vertices. While being slower by a log k-factor in the exponent than the fastest known algorithm, given by Thilikos et al. (J Algorithms 56(1):1–24, 2005; J Algorithms 56(1):25–49, 2005), our algorithm has the advantage of being simpler and self-contained; arguably, it explains better the combinatorics of optimum-width layouts. © 2018, The Author(s).
Συγγραφείς:
Giannopoulou, A.C.
Pilipczuk, M.
Raymond, J.-F.
Thilikos, D.M.
Wrochna, M.
Περιοδικό:
Algorithmica (New York)
Εκδότης:
Springer New York LLC
Λέξεις-κλειδιά:
Algorithms, Algorithmic aspects; AS graph; Combinatorics; Cutwidths; Fixed-parameter algorithms; Fixed-parameter tractability; Immersions; Obstructions, Computer science
DOI:
10.1007/s00453-018-0424-7
