A Suite of Distributed Methodologies to Solve the Sparse Analytic Hierarchy Process Problem

Abstract

In this paper we aim at finding effective distributed algorithms to solve the Sparse Analytic Hierarchy Process (SAHP) problem, where a set of networked agents (e.g., wireless sensors, mobile robots or IoT devices) need to be ranked based on their utility/importance. However, instead of knowing their absolute importance, the agents know their relative utility/importance with respect to their neighbors. Moreover, such a relative information is perturbed due to errors, subjective biases or incorrect information. Recently, the Sparse Eigenvector Method proved its effectiveness in tackling this problem. However, such a method has several drawbacks, such as demanding computation/communication requirements and lack of control on the magnitude of the computed estimate. With the aim to mitigate such issues, in this paper we inspect the possibility to resort to a suite of different methodologies, each inspired to well known algorithms in the literature, i.e., Metropolis-Hastings Markov chains, Heat-Bath Markov chains and formation control. The proposed methodologies are less demanding in terms of memory and communication capabilities; however, each approach has its own strength points and drawbacks. The aim of this paper is thus to provide a numerical comparison of their performances over networks with different characteristics.