Random Walks in Routing Landscapes

Title: Random Walks in Routing Landscapes

Abstract: This research paper presents a combinatorial optimization view on the routing problem for connectionless packet networks using the metaphor of a landscape. It examines the main properties of routing landscapes and how they can help in evaluating the problem's difficulty and generating effective algorithms. It also presents the random walk statistical technique to evaluate the main properties of these landscapes and provides examples to demonstrate its use.

Main Research Question: How can the theory of landscapes be used to understand and solve the routing problem in packet networks?

Methodology: The study uses the theory of landscapes, a framework from biology that is used to think about evolution. It defines three basic components of a landscape: the solutions space, a neighboring relationship, and a "fitness" function. The solutions space is the set of possible solutions, the neighboring relationship defines which points are neighbors, and the fitness function defines a partial ordering on the solution space. The researchers apply this theory to the routing problem by defining the solutions space as the set of possible routes, the neighboring relationship as the ability to inter-convert routes by simple operations, and the fitness function as the total length of a route.

Results: The study shows that the random walk statistical technique can be used to evaluate the main properties of the routing landscapes. It also provides examples to demonstrate the use of the technique in the context of the routing problem.

Implications: The research suggests that the theory of landscapes can be used to understand the complexity of the routing problem and to develop effective heuristics for solving it. The random walk technique can be used to evaluate the properties of the routing landscapes and to guide the development of heuristics. The study also highlights the importance of considering partial network state information and statistical shifts in the routing problem.

Link to Article: https://arxiv.org/abs/0109028v1 Authors: arXiv ID: 0109028v1