The structure and number of global roundings of a graph

Tetsuo Asano; Naoki Katoh; Hisao Tamaki; Takeshi Tokuyama

doi:10.1016/j.tcs.2004.02.044

The structure and number of global roundings of a graph

Tetsuo Asano, Naoki Katoh, Hisao Tamaki, Takeshi Tokuyama

INF - System Information Sciences

Research output: Contribution to journal › Conference article › peer-review

3 Citations (Scopus)

Abstract

Given a connected weighted graph G = (V, E), we consider a hypergraph H_G = (V, script P sign _G) corresponding to the set of all shortest paths in G. For a given real assignment a on V satisfying 0≤a(v)≤1, a global rounding a with respect to H_G is a binary assignment satisfying that |Σ_u∈Fa(v) - α(v)| - < 1 for every F ∈ script P sign _G. We conjecture that there are at most |V| + 1 global roundings for H_G, and also the set of global roundings is an affine independent set. We give several positive evidences for the conjecture.

Original language	English
Pages (from-to)	425-437
Number of pages	13
Journal	Theoretical Computer Science
Volume	325
Issue number	3
DOIs	https://doi.org/10.1016/j.tcs.2004.02.044
Publication status	Published - 2004 Oct 6
Event	Selected Papers from COCOON 2003 - Big Sky, United States Duration: 2003 Jul 25 → 2003 Jul 28

Keywords

Combinatorics
Discrepancy
Graph
Hypergraph
Rounding

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

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title = "The structure and number of global roundings of a graph",

abstract = "Given a connected weighted graph G = (V, E), we consider a hypergraph HG = (V, script P sign G) corresponding to the set of all shortest paths in G. For a given real assignment a on V satisfying 0≤a(v)≤1, a global rounding a with respect to HG is a binary assignment satisfying that |Σu∈Fa(v) - α(v)| - < 1 for every F ∈ script P sign G. We conjecture that there are at most |V| + 1 global roundings for HG, and also the set of global roundings is an affine independent set. We give several positive evidences for the conjecture.",

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T1 - The structure and number of global roundings of a graph

AU - Asano, Tetsuo

AU - Katoh, Naoki

AU - Tamaki, Hisao

AU - Tokuyama, Takeshi

PY - 2004/10/6

Y1 - 2004/10/6

N2 - Given a connected weighted graph G = (V, E), we consider a hypergraph HG = (V, script P sign G) corresponding to the set of all shortest paths in G. For a given real assignment a on V satisfying 0≤a(v)≤1, a global rounding a with respect to HG is a binary assignment satisfying that |Σu∈Fa(v) - α(v)| - < 1 for every F ∈ script P sign G. We conjecture that there are at most |V| + 1 global roundings for HG, and also the set of global roundings is an affine independent set. We give several positive evidences for the conjecture.

AB - Given a connected weighted graph G = (V, E), we consider a hypergraph HG = (V, script P sign G) corresponding to the set of all shortest paths in G. For a given real assignment a on V satisfying 0≤a(v)≤1, a global rounding a with respect to HG is a binary assignment satisfying that |Σu∈Fa(v) - α(v)| - < 1 for every F ∈ script P sign G. We conjecture that there are at most |V| + 1 global roundings for HG, and also the set of global roundings is an affine independent set. We give several positive evidences for the conjecture.

KW - Combinatorics

KW - Discrepancy

KW - Graph

KW - Hypergraph

KW - Rounding

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DO - 10.1016/j.tcs.2004.02.044

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JO - Theoretical Computer Science

JF - Theoretical Computer Science

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T2 - Selected Papers from COCOON 2003

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The structure and number of global roundings of a graph

Abstract

Keywords

ASJC Scopus subject areas

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