Efficient labeling algorithms for adjacent quadratic shortest paths

12/07/2021
by   João Vilela, et al.
0

In this article, we study the Adjacent Quadratic Shortest Path Problem (AQSPP), which consists in finding the shortest path on a directed graph when its total weight component also includes the impact of consecutive arcs. We provide a formal description of the AQSPP and propose an extension of Dijkstra's algorithm (that we denote aqD) for solving AQSPPs in polynomial-time and provide a proof for its correctness under some mild assumptions. Furthermore, we introduce an adjacent quadratic A* algorithm (that we denote aqA*) with a backward search for cost-to-go estimation to speed up the search. We assess the performance of both algorithms by comparing their relative performance with benchmark algorithms from the scientific literature and carry out a thorough collection of sensitivity analysis of the methods on a set of problem characteristics using randomly generated graphs. Numerical results suggest that: (i) aqA* outperforms all other algorithms, with a performance being about 75 times faster than aqD and the fastest alternative; (ii) the proposed solution procedures do not lose efficiency when the magnitude of quadratic costs vary; (iii) aqA* and aqD are fastest on random graph instances, compared with benchmark algorithms from scientific literature. We conclude the numerical experiments by presenting a stress test of the AQSPP in the context of real grid graph instances, with sizes up to 16 × 10^6 nodes, 64 × 10^6 arcs, and 10^9 quadratic arcs.

READ FULL TEXT

page 8

page 9

page 10

research
08/19/2019

A New Fast Unweighted All-pairs Shortest Path Search Algorithm Based on Pruning by Shortest Path Trees

We present a new fast all-pairs shortest path algorithm for unweighted g...
research
09/19/2023

K-Shortest Simple Paths Using Biobjective Path Search

In this paper we introduce a new algorithm for the k-Shortest Simple Pat...
research
04/17/2020

The two player shortest path network interdiction problem

In this article, we study a biobjective extension of the shortest path n...
research
08/19/2019

A New Fast Weighted All-pairs Shortest Path Search Algorithm Based on Pruning by Shortest Path Trees

Recently we submitted a paper, whose title is A New Fast Unweighted All-...
research
07/29/2023

Search for shortest paths based on the projective description of unweighted graphs

A new method of representing graph projections in computer memory is pro...
research
12/25/2020

Graph500 from OCaml-Multicore Perspective

OCaml is an industrial-strength, multi-paradigm programming language, wi...

Please sign up or login with your details

Forgot password? Click here to reset