TY - GEN

T1 - Relationship between Approximability and request structures in the minimum certificate dispersal problem

AU - Izumi, Tomoko

AU - Izumi, Taisuke

AU - Ono, Hirotaka

AU - Wada, Koichi

N1 - Copyright:
Copyright 2010 Elsevier B.V., All rights reserved.

PY - 2009

Y1 - 2009

N2 - Given a graph G=(V,E) and a set R ⊆ V ×V of requests, we consider to assign a set of edges to each node in G so that for every request (u, v) in R the union of the edge sets assigned to u and v contains a path from u to v. The Minimum Certificate Dispersal Problem (MCD) is defined as one to find an assignment that minimizes the sum of the cardinality of the edge set assigned to each node. In this paper, we give an advanced investigation about the difficulty of MCD by focusing on the relationship between its (in)approximability and request structures. We first show that MCD with general R has Θ(logn) lower and upper bounds on approximation ratio under the assumption P≠NP, where n is the number of nodes in G. We then assume R forms a clique structure, called Subset-Full, which is a natural setting in the context of the application. Interestingly, under this natural setting, MCD becomes to be 2-approximable, though it has still no polynomial time approximation algorithm whose factor better than 677/676 unless P=NP. Finally, we show that this approximation ratio can be improved to 3/2 for undirected variant of MCD with Subset-Full.

AB - Given a graph G=(V,E) and a set R ⊆ V ×V of requests, we consider to assign a set of edges to each node in G so that for every request (u, v) in R the union of the edge sets assigned to u and v contains a path from u to v. The Minimum Certificate Dispersal Problem (MCD) is defined as one to find an assignment that minimizes the sum of the cardinality of the edge set assigned to each node. In this paper, we give an advanced investigation about the difficulty of MCD by focusing on the relationship between its (in)approximability and request structures. We first show that MCD with general R has Θ(logn) lower and upper bounds on approximation ratio under the assumption P≠NP, where n is the number of nodes in G. We then assume R forms a clique structure, called Subset-Full, which is a natural setting in the context of the application. Interestingly, under this natural setting, MCD becomes to be 2-approximable, though it has still no polynomial time approximation algorithm whose factor better than 677/676 unless P=NP. Finally, we show that this approximation ratio can be improved to 3/2 for undirected variant of MCD with Subset-Full.

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U2 - 10.1007/978-3-642-02882-3_7

DO - 10.1007/978-3-642-02882-3_7

M3 - Conference contribution

AN - SCOPUS:76249130474

SN - 3642028810

SN - 9783642028816

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 56

EP - 65

BT - Computing and Combinatorics - 15th Annual International Conference, COCOON 2009, Proceedings

T2 - 15th Annual International Conference on Computing and Combinatorics, COCOON 2009

Y2 - 12 July 2009 through 14 July 2009

ER -