Efficiently listing bounded length st-paths
Romeo Rizzi, Gustavo Sacomoto, Marie-France Sagot

TL;DR
This paper introduces new algorithms for listing all simple $st$-paths in a graph with bounded length, achieving similar time complexity to classic methods but with significantly reduced space requirements.
Contribution
It presents a novel length-bounded $st$-path listing algorithm with optimal time complexity and a unified framework connecting classic and new path enumeration methods.
Findings
Algorithms match classic time complexities
Reduced space complexity to O(m+n)
Unified traversal framework for different parameterizations
Abstract
The problem of listing the shortest simple (loopless) -paths in a graph has been studied since the early 1960s. For a non-negatively weighted graph with vertices and edges, the most efficient solution is an algorithm for directed graphs by Yen and Lawler [Management Science, 1971 and 1972], and an algorithm for the undirected version by Katoh et al. [Networks, 1982], both using space. In this work, we consider a different parameterization for this problem: instead of bounding the number of -paths output, we bound their length. For the bounded length parameterization, we propose new non-trivial algorithms matching the time complexity of the classic algorithms but using only space. Moreover, we provide a unified framework such that the solutions to both parameterizations -- the classic -shortest and the…
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Taxonomy
TopicsAdvanced Graph Theory Research · Complexity and Algorithms in Graphs · Interconnection Networks and Systems
