Results 1  10
of
17
A Faster Algorithm for Solving OneClock Priced Timed Games
"... Oneclock priced timed games is a class of twoplayer, zerosum, continuoustime games that was defined and thoroughly studied in previous works. We show that Oneclock priced timed games can be solved in time m12 n n O(1) , where n is the number of states and m is the number of actions. The best pr ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
(Show Context)
Oneclock priced timed games is a class of twoplayer, zerosum, continuoustime games that was defined and thoroughly studied in previous works. We show that Oneclock priced timed games can be solved in time m12 n n O(1) , where n is the number of states and m is the number of actions. The best previously known time bound for solving oneclock priced timed games was 2 O(n2 +m), due to Rutkowski. For our improvement, we introduce and study a new algorithm for solving Oneclock Priced Timed Games, based on the sweepline technique from computational geometry. The analysis is based on the strategy iteration paradigm from the algorithmic theory of Markov decision processes. As a corollary, we also improve the analysis of previous algorithms due to Bouyer, Cassez, Fleury, and Larsen; and Alur, Bernadsky, and Madhusudan.
Interdiction problems on planar graphs
 In Proc. 16th APPROXRANDOM, volume 8096 of LNCS
, 2013
"... ar ..."
(Show Context)
Complexity of determining the most vital elements for the 1median and 1center location problems
"... ..."
Network interdiction – models, applications, unexplored directions
, 2010
"... Network interdiction is the monitoring or halting of an adversary’s activity on a network. Its models involve two players, usually called the interdictor and the evader (or, in the more general context of Stackelberg games, leader and follower). The evader operates on the network to optimize some ob ..."
Abstract
 Add to MetaCart
(Show Context)
Network interdiction is the monitoring or halting of an adversary’s activity on a network. Its models involve two players, usually called the interdictor and the evader (or, in the more general context of Stackelberg games, leader and follower). The evader operates on the network to optimize some objective such as moving through the network as fast as possible (shortest path interdiction), or with as little probability of being detected as possible (most reliable path interdiction), or to maximize the amount of goods transported through the network (network flow interdiction). The interdictor has the capacity to change the structure or parameters of the network (remove vertices or edges, increase detection probabilities, or lower arc capacities) in order to minimize the evader’s objective function. The study of network interdiction began with military applications: disruption of the flow of enemy troops. More recent applications include infectious disease control, counterterrorism, interception of contraband and illegal items such as drugs, weapons, or nuclear material, and the monitoring of computer networks. A large variety of models have been proposed for different interdiction problems. These include combinatorial optimization, stochastic programming, and game theoretic approaches. In this note we attempt to collect the most researched models, match them with applications, and summarize the latest algorithmic and complexity results. In Section 1 we introduce the basic ideas and define the necessary terms. Section 2 is concerned with various models that have been proposed in the literature, as well as with algorithms and complexity bounds. In Section 3 we examine which models would be appropriate for which applications. Finally, in Section 4 we outline two promising research directions for the future. 1
Path coalitional games
"... Abstract. We present a general framework to model strategic aspects and stable and fair resource allocations in networks via variants and generalizations of path coalitional games. In these games, a coalition of edges or vertices is successful if it can enable an st path. We present polynomialtime ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. We present a general framework to model strategic aspects and stable and fair resource allocations in networks via variants and generalizations of path coalitional games. In these games, a coalition of edges or vertices is successful if it can enable an st path. We present polynomialtime algorithms to compute and verify least core payoffs of costbased generalizations of path coalitional games and their duals, thereby settling a number of open problems. The least core payoffs of path coalitional games are completely characterized and a polynomialtime algorithm for computing the nucleolus of edge path coalitional games on undirected seriesparallel graphs is presented. 1
A Matheuristic for LeaderFollower Games Involving Facility LocationProtectionInterdiction Decisions
"... Abstract The topic of this chapter is the application of a matheuristic to the leaderfollower type of games—also called static Stackelberg games—that occur in the context of discrete location theory. The players of the game are a system planner (the leader) and an attacker (the follower). The decis ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract The topic of this chapter is the application of a matheuristic to the leaderfollower type of games—also called static Stackelberg games—that occur in the context of discrete location theory. The players of the game are a system planner (the leader) and an attacker (the follower). The decisions of the former are related to locating/relocating facilities as well as protecting some of those to provide service. The attacker, on the other hand, is interested in destroying (interdicting) facilities to cause the maximal possible disruption in service provision or accessibility. The motivation in the presented models is to identify the facilities that are most likely to be targeted by the attacker, and to devise a protection plan to minimize the resulting disruption on coverage as well as median type supply/demand or service networks. Stackelberg games can be formulated as a bilevel programming problem where the upper and the lower level problems with conflicting objectives belong to the leader and the follower, respectively. In this chapter, we first discuss the state of the art of the existing literature on both facility and network interdiction problems. Secondly, we present two fixedcharge facility locationprotectioninterdiction models
A Refined Complexity Analysis of Finding the Most Vital Edges for Undirected Shortest Paths
"... We study the NPhard Shortest Path Most Vital Edges problem arising in the context of analyzing network robustness. For an undirected graph with positive integer edge lengths and two designated vertices s and t, the goal is to delete as few edges as possible in order to increase the length of the ..."
Abstract
 Add to MetaCart
(Show Context)
We study the NPhard Shortest Path Most Vital Edges problem arising in the context of analyzing network robustness. For an undirected graph with positive integer edge lengths and two designated vertices s and t, the goal is to delete as few edges as possible in order to increase the length of the (new) shortest stpath as much as possible. This scenario has been mostly studied from the viewpoint of approximation algorithms and heuristics, while we particularly introduce a parameterized and multivariate point of view. We derive refined tractability as well as hardness results, and identify numerous directions for future research. Among other things, we show that increasing the shortest path length by at least one is much easier than to increase it by at least two.