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
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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 -