32 research outputs found
Polynomial Time Algorithm for Determining Max-Min Paths in Networks and Solving Zero Value Cyclic Games
We study the max-min paths problem, which represents a game version of the shortest and the longest paths problem in a weighted directed graph. In this problem the vertex set V of the weighted directed graph G=(V,E) is divided into two disjoint subsets VA and VB which are regarded as positional sets of two players. The players are seeking for a directed path from the given starting position ν 0 to the final position ν f , where the first player intends to maximize the integral cost of the path while the second one has aim to minimize it. Polynomial-time algorithm for determining max-min path in networks is proposed and its application for solving zero value cyclic games is developed.
Mathematics Subject Classification 2000: 90B10, 90C35, 90C27
Algorithms for solving discrete control problems on networks
We consider the discrete optimal problem on networks with integral-time cost criterion by a trajectory when the starting and final states of the system are fixed. A polynomial-time algorithm for solving this problem is proposed
Algorithms for finding the minimum cycle mean in the weighted directed graph
In this paper we study the problem of finding the minimum cycle mean in the weighted directed graph. The computational aspect of some algorithms for solving this problem is discussed and two algorithms for minimum cycle mean finding in the weighted directed graph are proposed
Linear programming approach for solving stochastic control problem on networks with discounted transition costs
Секция 10. Теоретическая информатикаThe infinite horizon stochastic control problem on network with expected total discounted cost optimization criterion is studied. A linear programming approach for solving this problem on networks is developed. Moreover, a polynomial tim
Algorithms for finding optimal paths in network games with p players
We study the problem of finding optimal paths in network games with p players. Some polynomial-time algorithms for finding optimal paths and optimal by Nash strategies of the players in network games with p players are proposed
Nodal dynamics, not degree distributions, determine the structural controllability of complex networks
Structural controllability has been proposed as an analytical framework for
making predictions regarding the control of complex networks across myriad
disciplines in the physical and life sciences (Liu et al.,
Nature:473(7346):167-173, 2011). Although the integration of control theory and
network analysis is important, we argue that the application of the structural
controllability framework to most if not all real-world networks leads to the
conclusion that a single control input, applied to the power dominating set
(PDS), is all that is needed for structural controllability. This result is
consistent with the well-known fact that controllability and its dual
observability are generic properties of systems. We argue that more important
than issues of structural controllability are the questions of whether a system
is almost uncontrollable, whether it is almost unobservable, and whether it
possesses almost pole-zero cancellations.Comment: 1 Figures, 6 page
Equilibria-based Probabilistic Model Checking for Concurrent Stochastic Games
Probabilistic model checking for stochastic games enables formal verification
of systems that comprise competing or collaborating entities operating in a
stochastic environment. Despite good progress in the area, existing approaches
focus on zero-sum goals and cannot reason about scenarios where entities are
endowed with different objectives. In this paper, we propose probabilistic
model checking techniques for concurrent stochastic games based on Nash
equilibria. We extend the temporal logic rPATL (probabilistic alternating-time
temporal logic with rewards) to allow reasoning about players with distinct
quantitative goals, which capture either the probability of an event occurring
or a reward measure. We present algorithms to synthesise strategies that are
subgame perfect social welfare optimal Nash equilibria, i.e., where there is no
incentive for any players to unilaterally change their strategy in any state of
the game, whilst the combined probabilities or rewards are maximised. We
implement our techniques in the PRISM-games tool and apply them to several case
studies, including network protocols and robot navigation, showing the benefits
compared to existing approaches
Equilibria-based probabilistic model checking for concurrent stochastic games
Probabilistic model checking for stochastic games enables formal verification of systems that comprise competing or collaborating entities operating in a stochastic environment. Despite good progress in the area, existing approaches focus on zero-sum goals and cannot reason about scenarios where entities are endowed with different objectives. In this paper, we propose probabilistic model checking techniques for concurrent stochastic games based on Nash equilibria. We extend the temporal logic rPATL (probabilistic alternating-time temporal logic with rewards) to allow reasoning about players with distinct quantitative goals, which capture either the probability of an event occurring or a reward measure. We present algorithms to synthesise strategies that are subgame perfect social welfare optimal Nash equilibria, i.e., where there is no incentive for any players to unilaterally change their strategy in any state of the game, whilst the combined probabilities or rewards are maximised. We implement our techniques in the PRISM-games tool and apply them to several case studies, including network protocols and robot navigation, showing the benefits compared to existing approaches