Finding the cost-optimal path with time constraint over time-dependent graphs

Abstract

Shortest path query is an important problem and has been well studied in static graphs. However, in practice, the costs of edges in graphs always change over time. We call such graphs as timedependent graphs. In this paper, we study how to find a costoptimal path with time constraint in time-dependent graphs. Most existing works regarding the Time-Dependent Shortest Path (TD-SP) problem focus on finding a shortest path with the minimum travel time. All these works are based on the following fact: the earliest arrival time at a vertex v can be derived from the earliest arrival time at v's neighbors. Unfortunately, this fact does not hold for our problem. In this paper, we propose a novel algorithm to compute a cost-optimal path with time constraint in time-dependent graphs. We show that the time and space complexities of our algorithm are O(kn log n + mk) and O((n + m)k) respectively. We confirm the effectiveness and efficiency of our algorithm through conducting experiments on real datasets with synthetic cost.

Full Solution Indexing for Top-K Web Service Composition

“…A linear-time algorithm is designed to compute the optimal path from originate to the terminate. Yang et al discuss the shortest-path problem with time constraint in timedependent graphs [16]. A TWO-STEP-SEARCH algorithm is proposed to solve this problem.…”

Cheapest paths in dynamic networks

“…Even in this work, optimal paths are allowed to contain cycles. In the authors look for an origin‐destination path with minimum cost and bounded total travel time. The network has piecewise constant costs on the arcs (with an upper bound on the number of intervals); free waiting times are allowed at all nodes.…”

Spaital query processing for location based services

“…The vehicles are charged if they pass through the major roads in rush hours. Similar policies are also applied in Singapore [128]. This results in the variation of the toll fee of a road in different hours of a day, which shows the toll fee is time-dependent.…”

“…The most relevant studies, [18], [128], and [10] solve cost-optimal problems under travel time constraints. Compared with the first two works ( [18,128]), they also allow waiting at a node and use dynamic programming to calculate the optimal cost, However, (i) they consider neither multiple costs, nor maximum speed constraints, and therefore the problem proposed in our work is novel; (ii) they either disallow waiting at any node or allow waiting at all nodes, but we only allow waiting at some nodes and at other nodes waiting is disallowed; (iii) our toll fee function could be any arbitrary single-valued function whereas [128] only allows the toll fee to be a piecewise constant function; (iii) our approach employs the technique of nonlinear programming optimization whereas [18,128] do not;…”

“…(iv) our paper can compute the optimal cost faster than [128], since our algorithm first computes the feasible arrival time interval and gains a topological sorting for the candidate nodes, which prunes much search space for recursively computing the optimal cost.…”