5,249 research outputs found
Faster Algorithms for Mean-Payoff Parity Games
Graph games provide the foundation for modeling and synthesis of reactive processes. Such games are played over graphs where the vertices are controlled by two adversarial players. We consider graph games where the objective of the first player is the conjunction of a qualitative objective (specified as a parity condition) and a quantitative objective (specified as a meanpayoff condition). There are two variants of the problem, namely, the threshold problem where the quantitative goal is to ensure that the mean-payoff value is above a threshold, and the value problem where the quantitative goal is to ensure the optimal mean-payoff value; in both cases ensuring the qualitative parity objective. The previous best-known algorithms for game graphs with n vertices, m edges, parity objectives with d priorities, and maximal absolute reward value W for mean-payoff objectives, are as follows: O(nd+1 . m . w) for the threshold problem, and O(nd+2 · m · W) for the value problem. Our main contributions are faster algorithms, and the running times of our algorithms are as follows: O(nd-1 · m ·W) for the threshold problem, and O(nd · m · W · log(n · W)) for the value problem. For mean-payoff parity objectives with two priorities, our algorithms match the best-known bounds of the algorithms for mean-payoff games (without conjunction with parity objectives). Our results are relevant in synthesis of reactive systems with both functional requirement (given as a qualitative objective) and performance requirement (given as a quantitative objective)
LIPIcs
Graph games provide the foundation for modeling and synthesis of reactive processes. Such games are played over graphs where the vertices are controlled by two adversarial players. We consider graph games where the objective of the first player is the conjunction of a qualitative objective (specified as a parity condition) and a quantitative objective (specified as a meanpayoff condition). There are two variants of the problem, namely, the threshold problem where the quantitative goal is to ensure that the mean-payoff value is above a threshold, and the value problem where the quantitative goal is to ensure the optimal mean-payoff value; in both cases ensuring the qualitative parity objective. The previous best-known algorithms for game graphs with n vertices, m edges, parity objectives with d priorities, and maximal absolute reward value W for mean-payoff objectives, are as follows: O(nd+1 . m . w) for the threshold problem, and O(nd+2 · m · W) for the value problem. Our main contributions are faster algorithms, and the running times of our algorithms are as follows: O(nd-1 · m ·W) for the threshold problem, and O(nd · m · W · log(n · W)) for the value problem. For mean-payoff parity objectives with two priorities, our algorithms match the best-known bounds of the algorithms for mean-payoff games (without conjunction with parity objectives). Our results are relevant in synthesis of reactive systems with both functional requirement (given as a qualitative objective) and performance requirement (given as a quantitative objective)
A Novel Clustering Algorithm Based on Quantum Games
Enormous successes have been made by quantum algorithms during the last
decade. In this paper, we combine the quantum game with the problem of data
clustering, and then develop a quantum-game-based clustering algorithm, in
which data points in a dataset are considered as players who can make decisions
and implement quantum strategies in quantum games. After each round of a
quantum game, each player's expected payoff is calculated. Later, he uses a
link-removing-and-rewiring (LRR) function to change his neighbors and adjust
the strength of links connecting to them in order to maximize his payoff.
Further, algorithms are discussed and analyzed in two cases of strategies, two
payoff matrixes and two LRR functions. Consequently, the simulation results
have demonstrated that data points in datasets are clustered reasonably and
efficiently, and the clustering algorithms have fast rates of convergence.
Moreover, the comparison with other algorithms also provides an indication of
the effectiveness of the proposed approach.Comment: 19 pages, 5 figures, 5 table
Using Strategy Improvement to Stay Alive
We design a novel algorithm for solving Mean-Payoff Games (MPGs). Besides
solving an MPG in the usual sense, our algorithm computes more information
about the game, information that is important with respect to applications. The
weights of the edges of an MPG can be thought of as a gained/consumed energy --
depending on the sign. For each vertex, our algorithm computes the minimum
amount of initial energy that is sufficient for player Max to ensure that in a
play starting from the vertex, the energy level never goes below zero. Our
algorithm is not the first algorithm that computes the minimum sufficient
initial energies, but according to our experimental study it is the fastest
algorithm that computes them. The reason is that it utilizes the strategy
improvement technique which is very efficient in practice
Non-oblivious Strategy Improvement
We study strategy improvement algorithms for mean-payoff and parity games. We
describe a structural property of these games, and we show that these
structures can affect the behaviour of strategy improvement. We show how
awareness of these structures can be used to accelerate strategy improvement
algorithms. We call our algorithms non-oblivious because they remember
properties of the game that they have discovered in previous iterations. We
show that non-oblivious strategy improvement algorithms perform well on
examples that are known to be hard for oblivious strategy improvement. Hence,
we argue that previous strategy improvement algorithms fail because they ignore
the structural properties of the game that they are solving
Finding all equilibria in games of strategic complements
I present a simple and fast algorithm that finds all the pure-strategy Nash equilibria in games with strategic complementarities. This is the first non-trivial algorithm for finding all pure-strategy Nash equilibria
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