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On Algorithms Employing Treewidth for L-bounded Cut Problems

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10384868" target="_blank" >RIV/00216208:11320/18:10384868 - isvavai.cz</a>

  • Result on the web

    <a href="http://jgaa.info/getPaper?id=462" target="_blank" >http://jgaa.info/getPaper?id=462</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.7155/jgaa.00462" target="_blank" >10.7155/jgaa.00462</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    On Algorithms Employing Treewidth for L-bounded Cut Problems

  • Original language description

    Given a graph G = (V, E) with two distinguished vertices s, t ELEMENT OF V and an integer parameter L &gt; 0, an L-bounded cut is a subset F of edges (vertices) such that the every path between s and t in GF has length more than L. The task is to find an L-bounded cut of minimum cardinality. Though the problem is very simple to state and has been studied since the beginning of the 70&apos;s, it is not much understood yet. The problem is known to be N P-hard to approximate within a small constant factor even for L GREATER-THAN OR EQUAL TO 4 (for L GREATER-THAN OR EQUAL TO 5 for the vertex-deletion version). On the other hand, the best known approximation algorithm for general graphs has approximation ratio only O(n^{2/3}) in the edge case, and O(sqrt n) in the vertex case, where n denotes the number of vertices. We show that for planar graphs, it is possible to solve both the edge- and the vertex-deletion version of the problem optimally in O((L+2)^{3L} n) time. That is, the problem is fixed-parameter tractable (FPT) with respect to L on planar graphs. Furthermore, we show that the problem remains FPT even for bounded genus graphs, a super class of planar graphs. Our second contribution deals with approximations of the vertex- deletion version of the problem. We describe an algorithm that for a given graph G, its tree decomposition of width τ and vertices s and t computes a τ -approximation of the minimum L-bounded s - t vertex cut; if the decomposition is not given, then the approximation ratio is O(τ sqrt{log τ}). For graphs with treewidth bounded by O(n 1/2-epsilon) for any epsilon &gt; 0, but not by a constant, this is the best approximation in terms of n that we are aware of.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS database

  • CEP classification

  • OECD FORD branch

    10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Result continuities

  • Project

    <a href="/en/project/GA15-11559S" target="_blank" >GA15-11559S: Extended Formulation of Polytopes</a><br>

  • Continuities

    P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Others

  • Publication year

    2018

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    Journal of Graph Algorithms and Applications

  • ISSN

    1526-1719

  • e-ISSN

  • Volume of the periodical

    22

  • Issue of the periodical within the volume

    2

  • Country of publishing house

    US - UNITED STATES

  • Number of pages

    15

  • Pages from-to

    177-191

  • UT code for WoS article

  • EID of the result in the Scopus database

    2-s2.0-85044206682