Fast Algorithms for Energy Games in Special Cases
Sebastian Forster (University of Salzburg), Antonis Skarlatos, (University of Salzburg), Tijn de Vos (University of Salzburg)

TL;DR
This paper introduces new algorithms for special cases of energy games, improving computational efficiency and providing insights into the complexity of solving these problems in reactive system analysis.
Contribution
The paper develops faster algorithms for specific energy game scenarios, including single-player cases and a variant of value iteration, advancing the understanding of their computational complexity.
Findings
Developed an $ ilde{O}(n^ ext{ω} W^ ext{ω})$ time algorithm for Alice-controlled graphs.
Provided an $ ilde{O}(n^ ext{ω} W^ ext{ω})$ algorithm for the APNP problem.
Presented a near-linear time algorithm for Bob-controlled graphs.
Abstract
In this paper, we study algorithms for special cases of energy games, a class of turn-based games on graphs that show up in the quantitative analysis of reactive systems. In an energy game, the vertices of a weighted directed graph belong either to Alice or to Bob. A token is moved to a next vertex by the player controlling its current location, and its energy is changed by the weight of the edge. Given a fixed starting vertex and initial energy, Alice wins the game if the energy of the token remains nonnegative at every moment. If the energy goes below zero at some point, then Bob wins. The problem of determining the winner in an energy game lies in . It is a long standing open problem whether a polynomial time algorithm for this problem exists. We devise new algorithms for three special cases of the problem. The first two results focus on the…
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Taxonomy
TopicsGraph Theory and Algorithms · Game Theory and Applications
