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A Fast Algorithm for (σ + 1)-Edge-Connectivity Augmentation of a σ-Edge-Connected Graph with Multipartition Constraints
en
Graduate School of Engineering, Hiroshima University
Graduate School of Engineering, Hiroshima University
Graduate School of Engineering, Hiroshima University
Tadachika Oki
Satoshi Taoka
Toshimasa Watanabe
The k-edge-connectivity augmentation problem with multipartition constraints (kECAM for short) is defined by “Given an undirected graph G = (V, E) and a multipartition π = {V1, . . . , Vr} of V with Vi ∩ Vj = ∅ for ∀i, j ∈ {1, . . . , r} (i ≠ j), find an edge set E' of minimum cardinality, consisting of edges that connect distinct members of π, such that G' = (V, E ∪ E') is k-edge-connected.”In this paper, we propose a fast algorithm for finding a solution to (σ+1)ECAM when G is σ-edge-connected (σ > 0), and show that the problem can be solved in linear time if σ ∈ {1, 2}. The main idea is to reduce (σ + 1)ECAM to the bipartition case, that is, (σ+1)ECAM with r = 2. Moreover, we propose a parallel algorithm for finding a solution to (σ + 1)ECAM, when a structural graph F(G) which represents all minimum cuts of G is given and σ is odd.
The k-edge-connectivity augmentation problem with multipartition constraints (kECAM for short) is defined by “Given an undirected graph G = (V, E) and a multipartition π = {V1, . . . , Vr} of V with Vi ∩ Vj = ∅ for ∀i, j ∈ {1, . . . , r} (i ≠ j), find an edge set E' of minimum cardinality, consisting of edges that connect distinct members of π, such that G' = (V, E ∪ E') is k-edge-connected.”In this paper, we propose a fast algorithm for finding a solution to (σ+1)ECAM when G is σ-edge-connected (σ > 0), and show that the problem can be solved in linear time if σ ∈ {1, 2}. The main idea is to reduce (σ + 1)ECAM to the bipartition case, that is, (σ+1)ECAM with r = 2. Moreover, we propose a parallel algorithm for finding a solution to (σ + 1)ECAM, when a structural graph F(G) which represents all minimum cuts of G is given and σ is odd.
AN1009593X
研究報告アルゴリズム（AL）
2010-AL-131
10
1-8
2010-09-15