IEICE TRANSACTIONS on Fundamentals
Efficient Algorithms to Augment the Edge-Connectivity of Specified Vertices by One in a Graph
Summary :
The k-edge-connectivity augmentation problem for a specified set of vertices (kECA-SV for short) is defined by “Given a graph G=(V, E) and a subset Γ ⊆ V, find a minimum set E' of edges such that G'=(V, E ∪ E') has at least k edge-disjoint paths between any pair of vertices in Γ.” Let σ be the edge-connectivity of Γ (that is, G has at least σ edge-disjoint paths between any pair of vertices in Γ). We propose an algorithm for (σ+1)ECA-SV which is done in O(|Γ|) maximum flow operations. Then the time complexity is O(σ2|Γ||V|+|E|) if a given graph is sparse, or O(|Γ||V||BG|log(|V|2/|BG|)+|E|) if dense, where |BG| is the number of pairs of adjacent vertices in G. Also mentioned is an O(|V||E|+|V|2 log |V|) time algorithm for a special case where σ is equal to the edge-connectivity of G and an O(|V|+|E|) time one for σ ≤ 2.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E102-A No.2 pp.379-388
- Publication Date
- 2019/02/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E102.A.379
- Type of Manuscript
- Special Section PAPER (Special Section on Mathematical Systems Science and its Applications)
- Category
Authors
Satoshi TAOKA
Hiroshima University
Toshimasa WATANABE
Hiroshima University
Keyword
Latest Issue
Copyrights notice of machine-translated contents
The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.
Cite this
Copy
Satoshi TAOKA, Toshimasa WATANABE, "Efficient Algorithms to Augment the Edge-Connectivity of Specified Vertices by One in a Graph" in IEICE TRANSACTIONS on Fundamentals,
vol. E102-A, no. 2, pp. 379-388, February 2019, doi: 10.1587/transfun.E102.A.379.
Abstract: The k-edge-connectivity augmentation problem for a specified set of vertices (kECA-SV for short) is defined by “Given a graph G=(V, E) and a subset Γ ⊆ V, find a minimum set E' of edges such that G'=(V, E ∪ E') has at least k edge-disjoint paths between any pair of vertices in Γ.” Let σ be the edge-connectivity of Γ (that is, G has at least σ edge-disjoint paths between any pair of vertices in Γ). We propose an algorithm for (σ+1)ECA-SV which is done in O(|Γ|) maximum flow operations. Then the time complexity is O(σ2|Γ||V|+|E|) if a given graph is sparse, or O(|Γ||V||BG|log(|V|2/|BG|)+|E|) if dense, where |BG| is the number of pairs of adjacent vertices in G. Also mentioned is an O(|V||E|+|V|2 log |V|) time algorithm for a special case where σ is equal to the edge-connectivity of G and an O(|V|+|E|) time one for σ ≤ 2.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E102.A.379/_p
Copy
@ARTICLE{e102-a_2_379,
author={Satoshi TAOKA, Toshimasa WATANABE, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Efficient Algorithms to Augment the Edge-Connectivity of Specified Vertices by One in a Graph},
year={2019},
volume={E102-A},
number={2},
pages={379-388},
abstract={The k-edge-connectivity augmentation problem for a specified set of vertices (kECA-SV for short) is defined by “Given a graph G=(V, E) and a subset Γ ⊆ V, find a minimum set E' of edges such that G'=(V, E ∪ E') has at least k edge-disjoint paths between any pair of vertices in Γ.” Let σ be the edge-connectivity of Γ (that is, G has at least σ edge-disjoint paths between any pair of vertices in Γ). We propose an algorithm for (σ+1)ECA-SV which is done in O(|Γ|) maximum flow operations. Then the time complexity is O(σ2|Γ||V|+|E|) if a given graph is sparse, or O(|Γ||V||BG|log(|V|2/|BG|)+|E|) if dense, where |BG| is the number of pairs of adjacent vertices in G. Also mentioned is an O(|V||E|+|V|2 log |V|) time algorithm for a special case where σ is equal to the edge-connectivity of G and an O(|V|+|E|) time one for σ ≤ 2.},
keywords={},
doi={10.1587/transfun.E102.A.379},
ISSN={1745-1337},
month={February},}
Copy
TY - JOUR
TI - Efficient Algorithms to Augment the Edge-Connectivity of Specified Vertices by One in a Graph
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 379
EP - 388
AU - Satoshi TAOKA
AU - Toshimasa WATANABE
PY - 2019
DO - 10.1587/transfun.E102.A.379
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E102-A
IS - 2
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - February 2019
AB - The k-edge-connectivity augmentation problem for a specified set of vertices (kECA-SV for short) is defined by “Given a graph G=(V, E) and a subset Γ ⊆ V, find a minimum set E' of edges such that G'=(V, E ∪ E') has at least k edge-disjoint paths between any pair of vertices in Γ.” Let σ be the edge-connectivity of Γ (that is, G has at least σ edge-disjoint paths between any pair of vertices in Γ). We propose an algorithm for (σ+1)ECA-SV which is done in O(|Γ|) maximum flow operations. Then the time complexity is O(σ2|Γ||V|+|E|) if a given graph is sparse, or O(|Γ||V||BG|log(|V|2/|BG|)+|E|) if dense, where |BG| is the number of pairs of adjacent vertices in G. Also mentioned is an O(|V||E|+|V|2 log |V|) time algorithm for a special case where σ is equal to the edge-connectivity of G and an O(|V|+|E|) time one for σ ≤ 2.
ER -
English
