arXiv subjects

Gautier Stauffer

Publications and source records attributed to Gautier Stauffer.

9 recordsLinked to original sources

arXiv2025

Faster Algorithms for the Least-Core value and the Nucleolus in Convex Games

The nucleolus is a central solution concept in cooperative game theory. While its computation is NP-hard in general, it can be computed in polynomial time for convex games; however, the only published polynomial-time algorithm relies on the ellipsoid method. We develop a combinatorial alternative based on reduced games and iterative least-core value computations. Leveraging submodular function minimization and polyhedral structure in a novel way, we obtain a faster combinatorial algorithm for computing the least-core value, improving the oracle complexity by a factor $n^3$ over previous approaches. As a consequence, we obtain a new strongly polynomial-time and combinatorial algorithm for computing the nucleolus in convex games. Preliminary analysis indicates an improved oracle complexity compared to the ellipsoid-based algorithm.

cs.GT↗

arXiv2024

Should Sports Professionals Consider Their Adversary's Strategy? A Case Study of Match Play in Golf

This study explores strategic considerations in professional golf's Match Play format, challenging the conventional focus on individual performance. Leveraging PGA Tour data, we investigate the impact of factoring in an adversary's strategy. Our findings suggest that while slight strategy adjustments can be advantageous in specific scenarios, the overall benefit of considering an opponent's strategy remains modest. This confirms the common wisdom in golf, reinforcing the recommendation to adhere to optimal stroke-play strategies due to challenges in obtaining precise opponent statistics. We believe that the methodology employed here could offer valuable insights into whether opponents' performances should also be considered in other two-player or team sports, such as tennis, darts, soccer, volleyball, etc. We hope that this research will pave the way for new avenues of study in these areas.

math.OC↗

arXiv2023

Golf Strategy Optimization and the "Drive for show, putt for dough" adage

This study explores strategic decision-making in professional golf's Stroke Play format through a computational lens. We develop a Markov Decision Process (MDP) model-specifically, a stochastic shortest path formulation-to optimize a golfer's strategy on any given course, incorporating both course layout and player skill data. While MDPs have been widely used in sports analytics, applying them to golf presents significant scalability challenges due to the curse of dimensionality. Our primary objective is not to predict player performance with high precision, but rather to demonstrate that an exact, data-driven MDP approach is computationally tractable on full scale, real-world instances. We show that, with careful problem structuring, low-level coding, and efficient memory management, it is possible to solve such large-scale models without resorting to heuristics or Q-learning approximations, as used in existing approaches. To illustrate the model's potential, we show how one can use PGA Tour data and aerial course imagery to simulate strategic outcomes and analyze how different skill profiles influence performance. In particular, we assess the relative impact of driving and putting, challenging the popular adage "Drive for show, putt for dough." These results support the value of our methodology as a robust proof of concept and a foundation for future enhancements. All code and analyses (in R and C++) are made available as open-source resources to support reproducibility and further research.

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arXiv2022

On the Nucleolus of a Class of Linear Production Games

We study the nucleolus in a class of cooperative games where agents collaborate by sharing demands and production-distribution capacities across multiple markets. These production-distribution games form a structured subclass of linear production games and capture applications such as horizontal collaboration in logistics. While computing the nucleolus is generally NP-hard for linear production games, we show that structural properties of production-distribution games enable efficient computation in several cases. Our main results focus on the uncapacitated variant. First, we provide a polynomial-time characterization of instances where the core reduces to a singleton, allowing direct computation of the nucleolus. Second, when the number of markets is fixed, we design a separation-based polynomial-time algorithm. Third, in the single-market case, we develop a faster combinatorial primal-dual algorithm that runs in $O(n^4)$.

cs.GT↗

arXiv2021

How many matchings cover the nodes of a graph?

Given an undirected graph, are there $k$ matchings whose union covers all of its nodes, that is, a matching-$k$-cover? A first, easy polynomial solution from matroid union is possible, as already observed by Wang, Song and Yuan (Mathematical Programming, 2014). However, it was not satisfactory neither from the algorithmic viewpoint nor for proving graphic theorems, since the corresponding matroid ignores the edges of the graph. We prove here, simply and algorithmically: all nodes of a graph can be covered with $k\ge 2$ matchings if and only if for every stable set $S$ we have $|S|\le k\cdot|N(S)|$. When $k=1$, an exception occurs: this condition is not enough to guarantee the existence of a matching-$1$-cover, that is, the existence of a perfect matching, in this case Tutte's famous matching theorem (J. London Math. Soc., 1947) provides the right `good' characterization. The condition above then guarantees only that a perfect $2$-matching exists, as known from another theorem of Tutte (Proc. Amer. Math. Soc., 1953). Some results are then deduced as consequences with surprisingly simple proofs, using only the level of difficulty of bipartite matchings. We give some generalizations, as well as a solution for minimization if the edge-weights are non-negative, while the edge-cardinality maximization of matching-$2$-covers turns out to be already NP-hard. We have arrived at this problem as the line graph special case of a model arising for manufacturing integrated circuits with the technology called `Directed Self Assembly'.

math.CO↗

arXiv2019

The $k$-path coloring problem in graphs with bounded treewidth: an application in integrated circuit manufacturing

In this paper, we investigate the $k$-path coloring problem, a variant of vertex coloring arising in the context of integrated circuit manufacturing. In this setting, typical industrial instances exhibit a `tree-like' structure. We exploit this property to design an efficient algorithm for our industrial problem: (i) on the methodological side, we show that the $k$-path coloring problem can be solved in polynomial time on graphs with bounded treewidth and we devise a simple polytime dynamic programming algorithm in this case (not relying on Courcelle's celebrated theorem); and (ii) on the empirical side, we provide computational evidences that the corresponding algorithm could be suitable for practice, by testing our algorithm on true instances obtained from an on-going collaboration with Mentor Graphics. We finally compare this approach with integer programming on some pseudo-industrial instances. It suggests that dynamic programming cannot compete with integer programming when the tree-width is greater than three. While all our industrial instances exhibit such a small tree-width, this is not for granted that all future instances will also do, and this tend to advocate for integer programming approaches.

cs.DM↗

arXiv2019

DSA-aware multiple patterning for the manufacturing of vias: Connections to graph coloring problems, IP formulations, and numerical experiments

In this paper, we investigate the manufacturing of vias in integrated circuits with a new technology combining lithography and Directed Self Assembly (DSA). Optimizing the production time and costs in this new process entails minimizing the number of lithography steps, which constitutes a generalization of graph coloring. We develop integer programming formulations for several variants of interest in the industry, and then study the computational performance of our formulations on true industrial instances. We show that the best integer programming formulation achieves good computational performance, and indicate potential directions to further speed-up computational time and develop exact approaches feasible for production.

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arXiv2017

The Stochastic Shortest Path Problem : A polyhedral combinatorics perspective

In this paper, we give a new framework for the stochastic shortest path problem in finite state and action spaces. Our framework generalizes both the frameworks proposed by Bertsekas and Tsitsikli and by Bertsekas and Yu. We prove that the problem is well-defined and (weakly) polynomial when (i) there is a way to reach the target state from any initial state and (ii) there is no transition cycle of negative costs (a generalization of negative cost cycles). These assumptions generalize the standard assumptions for the deterministic shortest path problem and our framework encapsulates the latter problem (in contrast with prior works). In this new setting, we can show that (a) one can restrict to deterministic and stationary policies, (b) the problem is still (weakly) polynomial through linear programming, (c) Value Iteration and Policy Iteration converge, and (d) we can extend Dijkstra's algorithm.

cs.DM↗

arXiv2011

On the Recognition of Fuzzy Circular Interval Graphs

Fuzzy circular interval graphs are a generalization of proper circular arc graphs and have been recently introduced by Chudnovsky and Seymour as a fundamental subclass of claw-free graphs. In this paper, we provide a polynomial-time algorithm for recognizing such graphs, and more importantly for building a suitable representation.

cs.DM↗