Labeling Methods for Partially Ordered Paths

by   Ricardo Euler, et al.

The landscape of applications and subroutines relying on shortest path computations continues to grow steadily. This growth is driven by the undeniable success of shortest path algorithms in theory and practice. It also introduces new challenges as the models and assessing the optimality of paths become more complicated. Hence, multiple recent publications in the field adapt existing labeling methods in an ad-hoc fashion to their specific problem variant without considering the underlying general structure: they always deal with multi-criteria scenarios and those criteria define different partial orders on the paths. In this paper, we introduce the partial order shortest path problem (POSP), a generalization of the multi-objective shortest path problem (MOSP) and in turn also of the classical shortest path problem. POSP captures the particular structure of many shortest path applications as special cases. In this generality, we study optimality conditions or the lack of them, depending on the objective functions' properties. Our final contribution is a big lookup table summarizing our findings and providing the reader an easy way to choose among the most recent multicriteria shortest path algorithms depending on their problem's weight structure. Examples range from time-dependent shortest path and bottleneck path problems to the fuzzy shortest path problem and complex financial weight functions studied in the public transportation community. Our results hold for general digraphs and therefore surpass previous generalizations that were limited to acyclic graphs.


Polynomial Time Prioritized Multi-Criteria k-Shortest Paths and k-Disjoint All-Criteria-Shortest Paths

The Shortest Path Problem, in real-life applications, has to deal with m...

PathWise: a flexible, open-source library for the Resource Constrained Shortest Path

In this paper, we consider a fundamental and hard combinatorial problem:...

Price Optimal Routing in Public Transportation

With the development of fast routing algorithms for public transit the o...

Enhanced Methods for the Weight Constrained Shortest Path Problem: Constrained Path Finding Meets Bi-objective Search

The classic problem of constrained path finding is a well-studied but ye...

Error Bounds for Discrete-Continuous Shortest Path Problems with Application to Free Flight Trajectory Optimization

Two-stage methods addressing continuous shortest path problems start loc...

User Preferences and the Shortest Path

Indoor navigation systems leverage shortest path algorithms to calculate...

Finding Control Synthesis for Kinematic Shortest Paths

This work presents the analysis of the properties of the shortest path c...

Please sign up or login with your details

Forgot password? Click here to reset