TY - JOUR

T1 - Better lower and upper bounds for the minimum rainbow subgraph problem

AU - Popa, Alexandru

N1 - Publisher Copyright:
© 2014 Elsevier B.V.
Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.

PY - 2014

Y1 - 2014

N2 - In this paper we study the minimum rainbow subgraph problem, motivated by applications in bioinformatics. The input of the problem consists of an undirected graph with n vertices where each edge is colored with one of the p possible colors. The goal is to find a subgraph of minimum order (i.e. minimum number of vertices) which has precisely one edge from each color class. In this paper we show a randomized max(√2n,√δ(1+√lnδ/2))-approximation algorithm using LP rounding, where δ is the maximum degree in the input graph. On the other hand we prove that there exists a constant c such that the minimum rainbow subgraph problem does not have a clnδ-approximation, unless NP⊆DTIME(nO(loglogn)).

AB - In this paper we study the minimum rainbow subgraph problem, motivated by applications in bioinformatics. The input of the problem consists of an undirected graph with n vertices where each edge is colored with one of the p possible colors. The goal is to find a subgraph of minimum order (i.e. minimum number of vertices) which has precisely one edge from each color class. In this paper we show a randomized max(√2n,√δ(1+√lnδ/2))-approximation algorithm using LP rounding, where δ is the maximum degree in the input graph. On the other hand we prove that there exists a constant c such that the minimum rainbow subgraph problem does not have a clnδ-approximation, unless NP⊆DTIME(nO(loglogn)).

KW - Approximation algorithms

KW - Combinatorial problems

KW - Minimum rainbow subgraph

UR - http://www.scopus.com/inward/record.url?scp=84909600118&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84909600118&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2014.05.008

DO - 10.1016/j.tcs.2014.05.008

M3 - Article

AN - SCOPUS:84909600118

VL - 543

SP - 1

EP - 8

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

IS - C

ER -