Neighbor Oblivious and Finite-State Algorithms for Circumventing Local Minima in Geographic Forwarding

TL;DR

This paper introduces neighbor oblivious, finite-state distributed algorithms for geographic routing that effectively avoid local minima and address integer overflow issues, ensuring loop-free, scalable network routing.

Contribution

It presents novel neighbor oblivious link reversal algorithms that do not require neighbor information and are designed to prevent integer overflow, with proven termination and bounded state size.

Findings

Algorithms successfully circumvent local minima in geographic routing.

States are bounded by logarithmic size, ensuring scalability.

One-bit and two-bit versions effectively prevent integer overflow.

Abstract

We propose distributed link reversal algorithms to circumvent communication voids in geographic routing. We also solve the attendant problem of integer overflow in these algorithms. These are achieved in two steps. First, we derive partial and full link reversal algorithms that do not require one-hop neighbor information, and convert a destination-disoriented directed acyclic graph (DAG) to a destination-oriented DAG. We embed these algorithms in the framework of Gafni and Bertsekas ("Distributed algorithms for generating loop-free routes in networks with frequently changing topology", 1981) in order to establish their termination properties. We also analyze certain key properties exhibited by our neighbor oblivious link reversal algorithms, e.g., for any two neighbors, their t-states are always consecutive integers, and for any node, its t-state size is upper bounded by log(N). In the second step, we resolve the integer overflow problem by analytically deriving one-bit full link reversal and two-bit partial link reversal versions of our neighbor oblivious link reversal algorithms.