On Algorithms Employing Treewidth for L-bounded Cut Problems

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

On Algorithms Employing Treewidth for L-bounded Cut Problems

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

On Algorithms Employing Treewidth for L-bounded Cut Problems

Popis výsledku anglicky

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.

Druh

J_SC - Článek v periodiku v databázi SCOPUS

CEP obor

—

OECD FORD obor

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

Projekt

<a href="/cs/project/GA15-11559S" target="_blank" >GA15-11559S: Rozšířené formulace polytopů</a><br>

Návaznosti

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

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

Journal of Graph Algorithms and Applications

ISSN

1526-1719

e-ISSN

—

Svazek periodika

22

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

15

Strana od-do

177-191

Kód UT WoS článku

—

EID výsledku v databázi Scopus

2-s2.0-85044206682