On Polynomial-Time Combinatorial Algorithms for Maximum L-Bounded Flow

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10420162" target="_blank" >RIV/00216208:11320/20:10420162 - isvavai.cz</a>

Result on the web

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=_Js47XY46d" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=_Js47XY46d</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.7155/jgaa.00534" target="_blank" >10.7155/jgaa.00534</a>

Result language

angličtina

Original language name

On Polynomial-Time Combinatorial Algorithms for Maximum L-Bounded Flow

Original language description

Given a graph G = (V, E) with two distinguished vertices s, (formula presented) and an integer L, an L-bounded flow is a flow between s and t that can be decomposed into paths of length at most L. In the maximum L-bounded flow problem the task is to find a maximum L-bounded flow between a given pair of vertices in the input graph. For networks with unit edge lengths (or, more generally, with polynomially bounded edge lengths, with respect to the number of vertices), the problem can be solved in polynomial time using linear programming. However, as far as we know, no polynomial-time combinatorial algorithm1 for the L-bounded flow is known. For general edge lengths, the problem is NP-hard. The only attempt, that we are aware of, to describe a combinatorial algorithm for the maximum L-bounded flow problem was done by Koubek and Říha in 1981. Unfortunately, their paper contains substantial flaws and the algorithm does not work; in the first part of this paper, we describe these problems. In the second part of this paper we describe a combinatorial algorithm based on the exponential length method that finds a (1+ε)-approximation of the maximum L-bounded flow in time O(ε-2 m2 L log L) where m is the number of edges in the graph. Moreover, we show that this approach works even for the NP-hard generalization of the maximum L-bounded flow problem in which each edge has a length.

Czech name

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Czech description

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Type

J_SC - Article in a specialist periodical, which is included in the SCOPUS database

CEP classification

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OECD FORD branch

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

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2020

Confidentiality

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

Name of the periodical

Journal of Graph Algorithms and Applications

ISSN

1526-1719

e-ISSN

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Volume of the periodical

24

Issue of the periodical within the volume

3

Country of publishing house

US - UNITED STATES

Number of pages

20

Pages from-to

303-322

UT code for WoS article

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EID of the result in the Scopus database

2-s2.0-85088278363