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

TL;DR

This paper introduces polynomial-time algorithms for finding prioritized multi-criteria and all-criteria-disjoint shortest secure paths in communication networks, addressing security and traffic bottleneck concerns.

Contribution

It presents novel polynomial-time algorithms for prioritized multi-criteria and $k$-disjoint shortest secure paths, expanding solutions for complex security-aware routing problems.

Findings

Polynomial-time algorithm for prioritized multi-criteria 2-disjoint paths.

Efficient solution for $k$-disjoint all-criteria-shortest secure paths.

Addresses security and traffic bottleneck issues in network routing.

Abstract

The shortest secure path (routing) problem in communication networks has to deal with multiple attack layers e.g., man-in-the-middle, eavesdropping, packet injection, packet insertion, etc. Consider different probabilities for each such attack over an edge, probabilities that can differ across edges. Furthermore, usage of a single shortest path (for routing) implies possible traffic bottleneck, which should be avoided if possible, which we term pathneck security avoidance. Finding all Pareto-optimal solutions for the multi-criteria single-source single-destination shortest secure path problem with non-negative edge lengths might yield a solution with an exponential number of paths. In the first part of this paper, we study specific settings of the multi-criteria shortest secure path problem, which are based on prioritized multi-criteria and on $k$-shortest secure paths. In the second part, we show a polynomial-time algorithm that, given an undirected graph $G$ and a pair of vertices $(s,t)$, finds prioritized multi-criteria $2$-disjoint (vertex/edge) shortest secure paths between $s$ and $t$. In the third part of the paper, we introduce the $k$-disjoint all-criteria-shortest secure paths problem, which is solved in time $O(\min(k|E|, |E|^{3/2}))$.