Adversarial Cooperative Path-Finding: Complexity and Algorithms

Ivanová, Marika; Surynek, Pavel

doi:10.1109/ictai.2014.22

Cited by 7 publications

(11 citation statements)

References 5 publications

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“…We have shown the lower bound for computational complexity of the APP problem, namely that it is PSPACE-hard. Theoretical study of ACPF (Ivanová and Surynek, 2014) showing its membership in EX-PTIME suggests that the same upper bound holds for APP but it is still an open question if APP is in PSPACE. In addition to complexity study we designed several practical algorithms for APP under the assumption of single-stage vertex allocation.…”

Section: Discussionmentioning

confidence: 99%

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Area Protection in Adversarial Path-finding Scenarios with Multiple Mobile Agents on Graphs - A Theoretical and Experimental Study of Strategies for Defense Coordination

Ivanová

Surynek

2018

Proceedings of the 10th International Conference on Agents and Artificial Intelligence

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We address a problem of area protection in graph-based scenarios with multiple agents. The problem consists of two adversarial teams of agents that move in an undirected graph shared by both teams. Agents are placed in vertices of the graph; at most one agent can occupy a vertex; and they can move into adjacent vertices in a conflict free way. Teams have asymmetric goals: the aim of one team -attackers -is to invade into given area while the aim of the opponent team -defenders -is to protect the area from being entered by attackers by occupying selected vertices. We study strategies for allocating vertices to be occupied by the team of defenders to block attacking agents. We show that the decision version of the problem of area protection is PSPACE-hard under the assumption that agents can allocate their target vertices multiple times. Further we develop various on-line vertex-allocation strategies for the defender team in a simplified variant of the problem with single stage vertex allocation and evaluated their performance in multiple benchmarks. The success of a strategy is heavily dependent on the type of the instance, and so one of the contributions of this work is that we identify suitable vertex-allocation strategies for diverse instance types. In particular, we introduce a simulation-based method that identifies and tries to capture bottlenecks in the graph, that are frequently used by the attackers. Our experimental evaluation suggests that this method often allows a successful defense even in instances where the attackers significantly outnumber the defenders.

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Section: Discussionmentioning

confidence: 99%

“…The technique of reduction of QBF to APP is inspired by a similar reduction of QBF to ACPF from which we borrow several technical steps and lemmas (Ivanová and Surynek, 2014). We describe the reduction from QBF using the following example.…”

Section: Theoretical Propertiesmentioning

confidence: 99%

Area Protection in Adversarial Path-finding Scenarios with Multiple Mobile Agents on Graphs - A Theoretical and Experimental Study of Strategies for Defense Coordination

Ivanová

Surynek

2018

Proceedings of the 10th International Conference on Agents and Artificial Intelligence

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“…The proof technique was partially inspired by Even's et al [6] proof of NP-completeness of the two-commodity integral flow problem [1]. Similarly as in [6], we reduce propositional satisfiability (SAT) [1,8,11] to optimal pCPF to show its NP-hardness. The reduction is quite complex and requires a thorough technical preparation, as elaborated in the following sections.…”

Section: The Intractability Of Optimal Cooperative Path-findingmentioning

confidence: 99%

“…The second property is the fact that all the clauses of the propositional formula in CNF [11] need to be satisfied in order to satisfy the entire formula. This characteristic will be called clause satisfaction.…”

Section: Overview Of the Reduction Of Sat To Optimal Pcpfmentioning

confidence: 99%

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On the Complexity of Optimal Parallel Cooperative Path-Finding

Surynek

2015

Fundamenta Informaticae

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A parallel version of the problem of cooperative path-finding (pCPF) is introduced in this paper. The task in CPF is to determine a spatio-temporal plan for each member of a group of agents. Each agent is given its initial location in the environment and its task is to reach the given goal location. Agents must avoid obstacles and must not collide with one another. The environment where agents are moving is modeled as an undirected graph. Agents are placed in vertices and they move along edges. At most one agent is placed in each vertex and at least one vertex remains unoccupied.An agent can only move into a currently unoccupied vertex in the standard version of CPF. In the parallel version, an agent can also move into a vertex being currently vacated by another agent supposing the character of this movement is not cyclic.The optimal pCPF where the task is to find the smallest possible solution of the makespan is particularly studied. The main contribution of this paper is the proof of NP-completeness of the decision version of the optimal pCPF. A reduction of propositional satisfiability (SAT) to the problem is used in the proof.

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Shared Multicast Trees in Ad Hoc Wireless Networks

Ivanová

2016

Lecture Notes in Computer Science

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This dissertation is a compilation of six research papers that are focused on three different topics summarized in the text. The first three papers address NP-hard problems arising in ad-hoc wireless communication discussed in Chapter 2. In general, the task is to broadcast a message in a given network of wireless devices while minimizing the power consumption. Problems in this category differ in requirements on the network connectivity, models of power consumption, and the ability of the devices to initiate a signal transmission. Some of the common features of these problems are that a device can simultaneously transmit a signal to all devices within its communication vicinity, and that a signal can travel from its originator to its recipient via multiple intermediate devices. The wireless networks are modeled and studied by means of graph theory. Solution techniques for these problems involve mainly methods of integer linear programming and inexact algorithms with or without performance guarantee. The next paper is focused on the problem of minimum broadcast time. Unlike the previous topic, the devices are in this problem supposed to send a signal to at most one neighbouring device at a time. The objective is to determine a sequence of signal transmission from a given set of source devices to the remaining ones, while minimizing the time needed for spreading the signal. Chapter 3 describes this problem in detail along with several related problems. The minimum broadcast time problem is also studied from the perspective of integer linear programming as well as the inexact algorithm perspective. Continuous relaxations of the ILP models help to evaluate the quality of the studied inexact methods. The stronger the model is, the more accurate assessment it provides. The last two papers are dedicated to problems belonging to path planning for multiple robots discussed in Chapter 4. In general, these problems involve a group of agents (robots) initially deployed in an environment. The task is to find a sequence of their moves so that they reach pre-defined destination locations while optimizing a given criterion such as minimum makespan or minimum total arrival time. The agents' movement must obey a set of given rules. An extension of the problem considers agents divided into two (or more) adversarial teams, where the teams have either symmetric or asymmetric objectives. After introducing the adversarial element, the problem of finding a winning strategy for a given team becomes PSPACE-hard, like many other two player games with alternating turns.

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Adversarial Cooperative Path-Finding: Complexity and Algorithms

Cited by 7 publications

References 5 publications

Area Protection in Adversarial Path-finding Scenarios with Multiple Mobile Agents on Graphs - A Theoretical and Experimental Study of Strategies for Defense Coordination

Area Protection in Adversarial Path-finding Scenarios with Multiple Mobile Agents on Graphs - A Theoretical and Experimental Study of Strategies for Defense Coordination

On the Complexity of Optimal Parallel Cooperative Path-Finding

Shared Multicast Trees in Ad Hoc Wireless Networks

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