Optimal Walks in Contact Sequence Temporal Graphs with No Zero Duration Cycle

Abstract

We develop an algorithm to find walks in contact sequence temporal graphs that have no cycle whose duration is zero. These walks minimize any specified linear combination of optimization criteria such as arrival time, travel duration, hops, and cost. The algorithm also accommodates waiting time constraints. When min and max waiting time constraints are specified, the complexity of our algorithm is $O(\vert V\vert +\vert E\vert\delta)$, where $\vert V\vert$ is the number of vertices, $\vert E\vert$ is the number of edges, and $\delta$ is the maximum out-degree of a vertex in the contact sequence temporal graph. When there are no maximum waiting time constraints, the complexity of our algorithm is $O(\vert V\vert +\vert E\vert)$. On the test data used by Bentert et al., our optimal walks algorithm provides a speedup of up to 77 over the algorithm of Bentert et al. [1] and a memory reduction of up to 3.2.