Competitive analysis of randomized online strategies for the multi-agent k-Canadian Traveler Problem

In this article, we study randomized online strategies for the multi-agent k-Canadian Traveler Problem which is defined on an undirected graph with a given source node O and a destination node D. Non-negative edge costs are given. The traveling agents are initially at O. There are k blocked edges in the graph, but these edges are not known to the agents. A blocked edge is learned when at least one of the agents arrives at one of its end-nodes. The objective is to find an online strategy such that at least one of the agents finds a route from O to D with minimum travel cost. We analyze the problem in three cases: (1) without communication, (2) with limited communication, and (3) with complete communication. We derive lower bounds on the competitive ratio of randomized online strategies for these cases. We show that increasing the number of agents can improve the competitive ratio of randomized online strategies when there is no communication between agents. We introduce a randomized online strategy which is optimal for both cases with limited and complete communication on O–D edge-disjoint graphs. We also prove that the competitive ratio of the optimal randomized strategy does not improve on O–D edge-disjoint graphs, when the case with complete communication is compared to the case with limited communication.