| Presentation | 2020-12-04 [Invited Talk] A Blossom Algorithm for Maximum Edge-Disjoint T-Paths Satoru Iwata, Yu Yokoi, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | Let $G=(V,E)$ be a multigraph with a set $Tsubseteq V$ of terminals. A path in $G$ is called a $T$-path if its ends are distinct vertices in $T$ and no internal vertices belong to $T$. In 1978, Mader showed a characterization of the maximum number of edge-disjoint $T$-paths. The original proof was not constructive, and hence it did not suggest an efficient algorithm. In this paper, we provide a combinatorial, deterministic algorithm for finding the maximum number of edge-disjoint $T$-paths. The algorithm adopts an augmenting path approach. More specifically, we introduce a novel concept of augmenting walks in auxiliary labeled graphs to capture a possible augmentation of the number of edge-disjoint $T$-paths. To design a search procedure for an augmenting walk, we introduce blossoms analogously to the blossom algorithm of Edmonds (1965) for the matching problem, while it is neither a special case nor a generalization of the present problem. When the search procedure terminates without finding an augmenting walk, the algorithm provides a certificate for the optimality of the current edge-disjoint $T$-paths. Thus the correctness argument of the algorithm serves as an alternative direct proof of Mader's theorem on edge-disjoint $T$-paths. The algorithm runs in $O(|V|cdot |E|^2)$ time, which is much faster than the best known deterministic algorithm based on a reduction to the linear matroid parity problem. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Combinatorial OptimizationGraph TheoryPolynomial Algorithm |
| Paper # | COMP2020-22 |
| Date of Issue | 2020-11-27 (COMP) |
| Conference Information | |
| Committee | COMP |
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| Conference Date | 2020/12/4(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Online |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Chair | Toshimitsu Masuzawa(Osaka Univ.) |
| Vice Chair | Hirotaka Ono(Nagoya Univ) |
| Secretary | Hirotaka Ono(NAIST) |
| Assistant | Yota Otachi(Nagoya Univ) |
| Paper Information | |
| Registration To | Technical Committee on Theoretical Foundations of Computing |
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| Language | ENG |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | [Invited Talk] A Blossom Algorithm for Maximum Edge-Disjoint T-Paths |
| Sub Title (in English) | |
| Keyword(1) | Combinatorial OptimizationGraph TheoryPolynomial Algorithm |
| 1st Author's Name | Satoru Iwata |
| 1st Author's Affiliation | University of Tokyo(Univ. of Tokyo) |
| 2nd Author's Name | Yu Yokoi |
| 2nd Author's Affiliation | National Institute of Informatics(NII) |
| Date | 2020-12-04 |
| Paper # | COMP2020-22 |
| Volume (vol) | vol.120 |
| Number (no) | COMP-276 |
| Page | pp.pp.28-28(COMP), |
| #Pages | 1 |
| Date of Issue | 2020-11-27 (COMP) |