Constrained Backward Time Travel Planning is in P

TL;DR

This paper explores the computational complexity of planning optimal travel routes in dynamic networks with backward time-travel devices, providing polynomial algorithms under certain constraints and analyzing pricing policies.

Contribution

It introduces exact polynomial-time algorithms for constrained backward time-travel planning in dynamic line graphs and analyzes pricing policies affecting these plans.

Findings

Polynomial algorithms for BTT-constrained planning

Impact analysis of pricing policies on planning

Optimal online algorithm for unconstrained BTT planning

Abstract

We consider transportation networks that are modeled by dynamic graphs, and introduce the possibility for traveling agents to use Backward Time-Travel (BTT) devices at any node to go back in time (to some extent, and with some appropriate fee) before resuming their trip. We focus on dynamic line graphs. In more detail, we propose exact algorithms to compute travel plans with constraints on the BTT cost or on how far back in time you can go, while minimizing travel delay (that is, the time difference between the arrival instant and the starting instant), in polynomial time. We study the impact of the BTT devices pricing policies on the computation process of those plans considering travel delay and cost, and provide necessary properties that pricing policies should satisfy to enable to compute such plans. Finally, we provide an optimal online algorithm for the unconstrained problem when the cost function is the identity.