IEICE TRANSACTIONS on Fundamentals
Approximation to the Minimum Cost Edge Installation Problem
Summary :
We consider the minimum cost edge installation problem (MCEI) in a graph G=(V,E) with edge weight w(e)≥ 0, e∈ E. We are given a vertex s∈ V designated as a sink, an edge capacity λ>0, and a source set S⊆ V with demand q(v)∈ [0,λ], v∈ S. For each edge e∈ E, we are allowed to install an integer number h(e) of copies of e. MCEI asks to send demand q(v) from each source v∈ S along a single path Pv to the sink s without splitting the demand of any source v∈ S. For each edge e∈ E, a set of such paths can pass through a single copy of e in G as long as the total demand along the paths does not exceed the edge capacity λ. The objective is to find a set P={Pv| v∈ S∈ of paths of G that minimizes the installing cost ∑e∈ E h(e)w(e). In this paper, we propose a (15/8+ρST)-approximation algorithm to MCEI, where ρST is any approximation ratio achievable for the Steiner tree problem.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E93-A No.4 pp.778-786
- Publication Date
- 2010/04/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E93.A.778
- Type of Manuscript
- PAPER
- Category
- Algorithms and Data Structures
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Ehab MORSY, Hiroshi NAGAMOCHI, "Approximation to the Minimum Cost Edge Installation Problem" in IEICE TRANSACTIONS on Fundamentals,
vol. E93-A, no. 4, pp. 778-786, April 2010, doi: 10.1587/transfun.E93.A.778.
Abstract: We consider the minimum cost edge installation problem (MCEI) in a graph G=(V,E) with edge weight w(e)≥ 0, e∈ E. We are given a vertex s∈ V designated as a sink, an edge capacity λ>0, and a source set S⊆ V with demand q(v)∈ [0,λ], v∈ S. For each edge e∈ E, we are allowed to install an integer number h(e) of copies of e. MCEI asks to send demand q(v) from each source v∈ S along a single path Pv to the sink s without splitting the demand of any source v∈ S. For each edge e∈ E, a set of such paths can pass through a single copy of e in G as long as the total demand along the paths does not exceed the edge capacity λ. The objective is to find a set P={Pv| v∈ S∈ of paths of G that minimizes the installing cost ∑e∈ E h(e)w(e). In this paper, we propose a (15/8+ρST)-approximation algorithm to MCEI, where ρST is any approximation ratio achievable for the Steiner tree problem.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E93.A.778/_p
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@ARTICLE{e93-a_4_778,
author={Ehab MORSY, Hiroshi NAGAMOCHI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Approximation to the Minimum Cost Edge Installation Problem},
year={2010},
volume={E93-A},
number={4},
pages={778-786},
abstract={We consider the minimum cost edge installation problem (MCEI) in a graph G=(V,E) with edge weight w(e)≥ 0, e∈ E. We are given a vertex s∈ V designated as a sink, an edge capacity λ>0, and a source set S⊆ V with demand q(v)∈ [0,λ], v∈ S. For each edge e∈ E, we are allowed to install an integer number h(e) of copies of e. MCEI asks to send demand q(v) from each source v∈ S along a single path Pv to the sink s without splitting the demand of any source v∈ S. For each edge e∈ E, a set of such paths can pass through a single copy of e in G as long as the total demand along the paths does not exceed the edge capacity λ. The objective is to find a set P={Pv| v∈ S∈ of paths of G that minimizes the installing cost ∑e∈ E h(e)w(e). In this paper, we propose a (15/8+ρST)-approximation algorithm to MCEI, where ρST is any approximation ratio achievable for the Steiner tree problem.},
keywords={},
doi={10.1587/transfun.E93.A.778},
ISSN={1745-1337},
month={April},}
Copy
TY - JOUR
TI - Approximation to the Minimum Cost Edge Installation Problem
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 778
EP - 786
AU - Ehab MORSY
AU - Hiroshi NAGAMOCHI
PY - 2010
DO - 10.1587/transfun.E93.A.778
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E93-A
IS - 4
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - April 2010
AB - We consider the minimum cost edge installation problem (MCEI) in a graph G=(V,E) with edge weight w(e)≥ 0, e∈ E. We are given a vertex s∈ V designated as a sink, an edge capacity λ>0, and a source set S⊆ V with demand q(v)∈ [0,λ], v∈ S. For each edge e∈ E, we are allowed to install an integer number h(e) of copies of e. MCEI asks to send demand q(v) from each source v∈ S along a single path Pv to the sink s without splitting the demand of any source v∈ S. For each edge e∈ E, a set of such paths can pass through a single copy of e in G as long as the total demand along the paths does not exceed the edge capacity λ. The objective is to find a set P={Pv| v∈ S∈ of paths of G that minimizes the installing cost ∑e∈ E h(e)w(e). In this paper, we propose a (15/8+ρST)-approximation algorithm to MCEI, where ρST is any approximation ratio achievable for the Steiner tree problem.
ER -
English
