Routing linear permutations on Fibonacci and Lucas cubes

TL;DR

This paper studies the problem of online routing linear permutations on Fibonacci and Lucas cubes, focusing on efficient message movement with constraints on queue length and synchronized steps.

Contribution

It introduces a routing model for Fibonacci and Lucas cubes and analyzes the routing of linear permutations under these constraints.

Findings

Routing algorithms for linear permutations on Fibonacci and Lucas cubes

Constraints on queue length and synchronized movement

Analysis of routing efficiency and complexity

Abstract

In recent years there has been much interest in certain subcubes of hypercubes, namely Fibonacci cubes and Lucas cubes (and their generalized versions). In this article we consider online routing of linear permutations on these cubes. The model of routing we use regards edges as bi-directional, and we do not allow queues of length greater than one. Messages start out at different vertices, and in movements synchronized with a clock, move to an adjacent vertex or remain where they are, so that at the next stage there is still exactly one message per vertex. This is the routing model we defined in an earlier paper.