Algorithms for deterministic parallel graph exploration

摘要: In this thesis we study the problem of parallel graph exploration using multiple synchronized mobile agents. Each agent is an entity that can, independently other agents, visit vertices and traverse its edges. The goal agents to all graph. We first in model where are equipped with internal memory but no available at nodes. Agents also allowed communicate between each by exchanging messages. present algorithms working a minimal possible time for team polynomial size (in number graph). impact range communication analysing which can arbitrary distance, or only located same node. efficient lower bounds almost match our positive results both models. consider when movements determined according so-called rotor-router mechanism. From perspective fixed node, sends out node along outgoing edges, ina round-robin fashion. speedup ratio worst-case single show speed up general graphs multi-agent always logarithmic linear tight analysis cycles, expanders, random graphs, cliques, constant dimensional tori almost-tight hypercubes. Finally collision-free exploration, has explore additional constraint two occupy time. case given map graph, optimal algorithm trees asymptotically graphs. have initial knowledge about close concluding remarks discussion related open problems area exploration.