Name
Abstract | ||
|---|---|---|
In this series of two papers we examine the classical problem of ranking a set of players on the basis of a set of pairwise comparisons arising from a sports tournament, with the objective of minimizing the total number of upsets, where an upset occurs if a higher ranked player was actually defeated by a lower ranked player. This problem can be rephrased as the so-called minimum feedback arc set problem on tournaments, which arises in a rich variety of applications and has been a subject of extensive research. In this series we study this NP-hard problem using structure-driven and linear programming approaches. Let T=(V,A) be a tournament with a nonnegative integral weight w(e) on each arc e. A subset F of arcs is called a feedback arc set if T\F contains no cycles (directed). A collection C of cycles (with repetition allowed) is called a cycle packing if each arc e is used at most w(e) times by members of C. We call T cycle Mengerian (CM) if, for every nonnegative integral function w defined on A, the minimum total weight of a feedback arc set is equal to the maximum size of a cycle packing. The purpose of these two papers is to show that a tournament is CM iff it contains none of four Möbius ladders as a subgraph; such a tournament is referred to as Möbius-free. In this first paper we present a structural description of all Möbius-free tournaments, which relies heavily on a chain theorem concerning internally 2-strong tournaments. |
Year | DOI | Venue |
|---|---|---|
2020 | 10.1016/j.jctb.2019.08.004 | Journal of Combinatorial Theory, Series B |
Keywords | DocType | Volume |
Tournament,Feedback arc set,Cycle packing,Minimax relation,Characterization | Journal | 141 |
ISSN | Citations | PageRank |
0095-8956 | 0 | 0.34 |
References | Authors | |
0 | 4 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Xujin Chen | 1 | 231 | 30.54 |
| Guoli Ding | 2 | 444 | 51.58 |
| Wenan Zang | 3 | 305 | 39.19 |
| Qiulan Zhao | 4 | 2 | 2.08 |