Possible Winners in Partially Completed Tournaments

Schwartz, Benjamin L.

doi:10.1137/1008062

Cited by 52 publications

(21 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The problem of determining when a sports team has mathematically clinched a playoff spot has been well studied for several sports, including baseball (Schwartz, 1966;Robinson, 1991;Wayne, 2001;Adler et al, 2002) and soccer (Ribeiro & Urrutia, 2005). The problem is known as a winner determination problem.…”

Section: Related Workmentioning

confidence: 99%

A hybrid constraint programming and enumeration approach for solving NHL playoff qualification and elimination problems

Russell

Beek

2012

European Journal of Operational Research

View full text Add to dashboard Cite

Many sports fans invest a great deal of time into watching and analyzing the performance of their favorite team. However, the tools at their disposal are primarily heuristic or based on folk wisdom. We provide a concrete mechanism for calculating the minimum number of points needed to guarantee a playoff spot and the minimum number of points needed to possibly qualify for a playoff spot in the National Hockey League (NHL). Our approach uses a combination of constraint programming, enumeration, network flows and decomposition to solve the problem efficiently. The technique can successfully be applied to any team at any point of the season to determine how well a team must do to make the playoffs.

show abstract

Section: Related Workmentioning

confidence: 99%

A hybrid constraint programming and enumeration approach for solving NHL playoff qualification and elimination problems

Russell

Beek

2012

European Journal of Operational Research

View full text Add to dashboard Cite

show abstract

“…First, we review how to determine whether or not a single team is eliminated. The following theorem is due to Schwartz [15].…”

Section: W(r)+g(r)mentioning

confidence: 99%

“…We construct a bipartite network in which feasible integral flows correspond to outcomes of the remaining schedule. The following network flow formulation is due to Schwartz [15]: Gusfield and Martel [10] give an alternate construction. There are nodes corresponding to teams and to remaining games.…”

Section: Theorem 22 Using a Single S-t Minimum Cut Computation We mentioning

confidence: 99%

“…Schwartz [15] proposed a method to determine whether a single team is eliminated using a maximum flow computation. Hoffman and Rivlin [11] generalized the result of [15], providing a characterization of when a team is eliminated from finishing in tth place.…”

Section: Introductionmentioning

confidence: 99%

“…Hoffman and Rivlin [11] generalized the result of [15], providing a characterization of when a team is eliminated from finishing in tth place. Robinson [14] gave a linear programming based model that finds the maximum lead a team can have at the end of the season.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A New Property and a Faster Algorithm for Baseball Elimination

Wayne¹

2001

SIAM J. Discrete Math.

View full text Add to dashboard Cite

Abstract. In the baseball elimination problem, there is a league consisting of n teams. At some point during the season, team i has w i wins and g ij games left to play against team j. A team is eliminated if it cannot possibly finish the season in first place or tied for first place. The goal is to determine exactly which teams are eliminated. The problem is not as easy as many sports writers would have you believe, in part because the answer depends not only on the number of games won and left to play but also on the schedule of remaining games. In the 1960's, Schwartz showed how to determine whether one particular team is eliminated using a maximum flow computation. This paper indicates that the problem is not as difficult as many mathematicians would have you believe. For each team i, let g i denote the number of games remaining. We prove that there exists a value W * such that team i is eliminated if and only if w i + g i < W * . Using this surprising fact, we can determine all eliminated teams in time proportional to a single maximum flow computation in a graph with n nodes; this improves upon the previous best known complexity bound by a factor of n.

show abstract

A new—old algorithm for minimum‐cut and maximum‐flow in closure graphs

Hochbaum

2001

Networks

View full text Add to dashboard Cite

We present an algorithm for solving the minimum-cut problem on closure graphs without maintaining flow values. The algorithm is based on an optimization algorithm for the open-pit mining problem that was presented in 1964 (and published in 1965) by Lerchs and Grossmann. The Lerchs-Grossmann algorithm (LG algorithm) solves the maximum closure which is equivalent to the minimum-cut problem. Yet, it appears substantially different from other algorithms known for solving the minimum-cut problem and does not employ any concept of flow. Instead, it works with sets of nodes that have a natural interpretation in the context of maximum closure in that they have positive total weight and are closed with respect to some subgraph. We describe the LG algorithm and study its features and the new insights it reveals for the maximum-closure problem and the maximum-flow problem. Specifically, we devise a linear time procedure that evaluates a feasible flow corresponding to any iteration of the algorithm. We show that while the LG algorithm is pseudopolynomial, our variant algorithms have complexity of O O O(mn mn mn log n n n), where n n n is the number of nodes and m m m is the number of arcs in the graph . Modifications of the algorithm allow for efficient sensitivity and parametric analysis also running in time O O O(mn mn mn log n n n).

show abstract

Possible Winners in Partially Completed Tournaments

Cited by 52 publications

References 1 publication

A hybrid constraint programming and enumeration approach for solving NHL playoff qualification and elimination problems

A hybrid constraint programming and enumeration approach for solving NHL playoff qualification and elimination problems

A New Property and a Faster Algorithm for Baseball Elimination

A new—old algorithm for minimum‐cut and maximum‐flow in closure graphs

Contact Info

Product

Resources

About