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DOI: 10.4230/LIPIcs.CP.2026.48

A Constraint Programming Approach for n-Day Lookahead Playoff Clinching in the NHL

Authors: Gili Rosenberg, Kyle E. C. Booth, J. Kyle Brubaker, and Ruben S. Andrist

Published in: LIPIcs, Volume 379, 32nd International Conference on Principles and Practice of Constraint Programming (CP 2026)

Abstract

In professional sports, a team has clinched the playoffs if they are guaranteed a postseason spot, regardless of the outcomes of any remaining games. As the season progresses, sports fans and other stakeholders are interested in precisely when, and under what conditions, their team will clinch the playoffs. In this paper, we investigate playoff clinching in the context of the National Hockey League (NHL), where it is computationally challenging to produce clinching scenarios due, in part, to complex tie-breakers. We present an algorithm that determines under which combinations of game outcomes in the next n days a team will clinch the playoffs (i.e., "n-day lookahead clinching"). Our approach is a custom tree search which employs various preprocessing techniques, pruning strategies, and node ordering heuristics to efficiently explore the space of possible outcomes. The tree search leverages a constraint programming (CP)-based subroutine for inference that determines if a team has clinched the playoffs for some snapshot in time of the regular season (i.e., "0-day lookahead clinching"). This CP subroutine aims to find a counter-example in which the team being evaluated is eliminated, taking into account qualification rules and the NHL’s extensive list of tie-breakers. We validate the efficacy of our algorithm using hundreds of scenarios based on public NHL data for the seasons 2021-22 through 2024-25. The methods introduced can be readily extended to other metrics of interest, including mathematical proof of playoff elimination, clinching the President’s Trophy, as well as clinching (or being eliminated from clinching) any other seed in the standings.

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Gili Rosenberg, Kyle E. C. Booth, J. Kyle Brubaker, and Ruben S. Andrist. A Constraint Programming Approach for n-Day Lookahead Playoff Clinching in the NHL. In 32nd International Conference on Principles and Practice of Constraint Programming (CP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 379, pp. 48:1-48:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{rosenberg_et_al:LIPIcs.CP.2026.48,
  author =	{Rosenberg, Gili and Booth, Kyle E. C. and Brubaker, J. Kyle and Andrist, Ruben S.},
  title =	{{A Constraint Programming Approach for n-Day Lookahead Playoff Clinching in the NHL}},
  booktitle =	{32nd International Conference on Principles and Practice of Constraint Programming (CP 2026)},
  pages =	{48:1--48:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-432-1},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{379},
  editor =	{Beldiceanu, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2026.48},
  URN =		{urn:nbn:de:0030-drops-266810},
  doi =		{10.4230/LIPIcs.CP.2026.48},
  annote =	{Keywords: Constraint programming, operations research, tree search, sports, hockey}
}

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Short Paper

DOI: 10.4230/LIPIcs.CP.2023.43

Constraint Programming Models for Depth-Optimal Qubit Assignment and SWAP-Based Routing (Short Paper)

Authors: Kyle E. C. Booth

Published in: LIPIcs, Volume 280, 29th International Conference on Principles and Practice of Constraint Programming (CP 2023)

Abstract

Due to the limited connectivity of gate model quantum devices, logical quantum circuits must be compiled to target hardware before they can be executed. Often, this process involves the insertion of SWAP gates into the logical circuit, usually increasing the depth of the circuit, achieved by solving a so-called qubit assignment and routing problem. Recently, a number of integer linear programming (ILP) models have been proposed for solving the qubit assignment and routing problem to proven optimality. These models encode the objective function and constraints of the problem, and leverage the use of automated solver technology to find hardware-compliant quantum circuits. In this work, we propose constraint programming (CP) models for this problem and compare their performance against ILP for circuit depth minimization for both linear and two-dimensional grid lattice device topologies on a set of randomly generated instances. Our empirical analysis indicates that the proposed CP approaches outperform the ILP models both in terms of solution quality and runtime.

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Kyle E. C. Booth. Constraint Programming Models for Depth-Optimal Qubit Assignment and SWAP-Based Routing (Short Paper). In 29th International Conference on Principles and Practice of Constraint Programming (CP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 280, pp. 43:1-43:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{booth:LIPIcs.CP.2023.43,
  author =	{Booth, Kyle E. C.},
  title =	{{Constraint Programming Models for Depth-Optimal Qubit Assignment and SWAP-Based Routing}},
  booktitle =	{29th International Conference on Principles and Practice of Constraint Programming (CP 2023)},
  pages =	{43:1--43:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-300-3},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{280},
  editor =	{Yap, Roland H. C.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2023.43},
  URN =		{urn:nbn:de:0030-drops-190805},
  doi =		{10.4230/LIPIcs.CP.2023.43},
  annote =	{Keywords: Qubit routing, quantum computing, constraint programming, combinatorial optimization}
}

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Documents authored by Booth, Kyle E. C.

A Constraint Programming Approach for n-Day Lookahead Playoff Clinching in the NHL

Abstract

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Constraint Programming Models for Depth-Optimal Qubit Assignment and SWAP-Based Routing (Short Paper)

Abstract

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