A Risk-Reward Competitive Analysis for the Recoverable Canadian Traveller Problem

摘要

From the online point of view, we study the Recoverable Canadian Traveller Problem (Recoverable-CTP) in a special network, in which the traveller knows in advance the structure of the network and the travel time of each edge. However, some edges may be blocked and the traveller only observes that upon reaching the vertex of the blocked edge, and the blocked edge may be reopened but the traveller doesn't know its recovery time. The goal is to find a least-cost route from the origin node to the destination node, more precisely, to find an adaptive strategy minimizing the ratio of traversed time to the travel time of the optimal offline shortest path (where all blocked edges and their recovery time are known in advance). We present an optimal online strategy - a comparison strategy and prove its competitive ratio. Moreover, with the different forecasts of the recovery time, some online strategies are given under the risk-reward framework, and the rewards and the risks of the different strategies are analysed.