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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

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

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

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

24

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

20

Strana od-do

303-322

Kód UT WoS článku

—

EID výsledku v databázi Scopus

2-s2.0-85088278363