Abstract
Identifying teams eliminated from contention for first place of a sports league is a much studied problem. In the classic setting each game is played between two teams, and the team with the most wins finishes first. Recently, two papers [Way] and [AEHO] detailed a surprising structural fact in the classic setting: At any point in the season, there is a computable threshold W such that a team is eliminated (cannot win or tie for first place) if and only if it cannot win W or more games. Using this threshold speeds up the identification of eliminated teams.
We show that thresholds exist for a wide range of elimination problems (greatly generalizing the classical setting), via a simpler and more direct proof. For the classic setting we determine which teams can be the strict winner of the most games; examine these issues for multi-division leagues with playoffs and wildcards; and establish that certain elimination questions are NP-hard.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
I. Adler, A. Erera, D. Hochbaum, and E. Olinich. Baseball, optimization and the world wide web. unpublished manuscript 1998.
T. Burnholt, A. Gullich, T. Hofmeister, and N. Schmitt. Football elimination is hard to decide under the 3-point rule. unpublished manuscript, 1999.
D. Gusfield and C. Martel. A fast algorithm for the generalized parametric minimum cut problem and applications. Algorithmica, 7:499–519, 1992.
D. Gusfield and C. Martel. The structure and complexity of sports elimination numbers. Technical Report CSE-99-1, http://www.theory.cs.ucdavis.edu/, Univ. of California, Davis, 1999.
A. Hoffman and J. Rivlin. When is a team “mathematically” eliminated? In H.W. Kuhn, editor, Princeton symposium on math programming (1967), pages 391–401. Princeton univ. press, 1970.
T. McCormick. Fast algorithms for parametric scheduling come from extensions to parametric maximum flow. Proc. of 28th ACM Symposium on the Theory of Computing, pages 394–422, 1996.
B. Schwartz. Possible winners in partially completed tournaments. SIAM Review, 8: 302–308, 1966.
K. Wayne. A new property and a faster algorithm for baseball elimination. ACM/SIAM Symposium on Discrete Algorithms, Jan. 1999.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gusfield, D., Martel, C. (1999). Thresholds for Sports Elimination Numbers: Algorithms and Complexity. In: Dehne, F., Sack, JR., Gupta, A., Tamassia, R. (eds) Algorithms and Data Structures. WADS 1999. Lecture Notes in Computer Science, vol 1663. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48447-7_33
Download citation
DOI: https://doi.org/10.1007/3-540-48447-7_33
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66279-2
Online ISBN: 978-3-540-48447-9
eBook Packages: Springer Book Archive