text: 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.
  @cite_12: Multi-agent path planning is a challenging problem with numerous real-life applications. Running a centralized search such as A* in the combined state space of all units is complete and cost-optimal, but scales poorly, as the state space size is exponential in the number of mobile units. Traditional decentralized approaches, such as FAR and WHCA*, are faster and more scalable, being based on problem decomposition. However, such methods are incomplete and provide no guarantees with respect to the running time or the solution quality. They are not necessarily able to tell in a reasonable time whether they would succeed in finding a solution to a given instance. We introduce MAPP, a tractable algorithm for multi-agent path planning on undirected graphs. We present a basic version and several extensions. They have low-polynomial worst-case upper bounds for the running time, the memory requirements, and the length of solutions. Even though all algorithmic versions are incomplete in the general case, each provides formal guarantees on problems it can solve. For each version, we discuss the algorithm's completeness with respect to clearly defined subclasses of instances. Experiments were run on realistic game grid maps. MAPP solved 99.86 of all mobile units, which is 18-22 better than the percentage of FAR and WHCA*. MAPP marked 98.82 of all units as provably solvable during the first stage of plan computation. Parts of MAPP's computation can be re-used across instances on the same map. Speed-wise, MAPP is competitive or significantly faster than WHCA*, depending on whether MAPP performs all computations from scratch. When data that MAPP can re-use are preprocessed offline and readily available, MAPP is slower than the very fast FAR algorithm by a factor of 2.18 on average. MAPP's solutions are on average 20 longer than FAR's solutions and 7-31 longer than WHCA*'s solutions.
  @cite_6: Multi-robot path planning is dificult due to the combinatorial explosion of the search space with every new robot added. Complete search of the combined state-space soon becomes intractable. In this paper we present a novel form of abstraction that allows us to plan much more eficiently. The key to this abstraction is the partitioning of the map into subgraphs of known structure with entry and exit restrictions which we can represent compactly. Planning then becomes a search in the much smaller space of subgraph configurations. Once an abstract plan is found, it can be quickly resolved into a correct (but possibly sub-optimal) concrete plan without the need for further search. We prove that this technique is sound and complete and demonstrate its practical effiectiveness on a real map. A contending solution, prioritised planning, is also evaluated and shown to have similar performance albeit at the cost of completeness. The two approaches are not necessarily conflicting; we demonstrate how they can be combined into a single algorithm which out-performs either approach alone.
  @cite_11: 
summary: Movements of agents at low reactive level are assumed to be planned by some cooperative path-finding - CPF ( multi-agent path-finding - MAPF) @cite_11 @cite_6 @cite_12 algorithm where agents of own team cooperate while opposing agents are considered as obstacles. In CPF the task is to plan movement of agents so that each agent reaches its unique target in a conflict free manner.