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arXiv2017

A Polynomial-time Algorithm for Detecting the Possibility of Braess Paradox in Directed Graphs

A directed multigraph is said vulnerable if it can generate Braess paradox in Traffic Networks. In this paper, we give a graph-theoretic characterisation of vulnerable directed multigraphs; analogous results appeared in the literature only for undirected multigraphs and for a specific family of directed multigraphs. The proof of our characterisation also provides an algorithm that checks if a multigraph is vulnerable in O(|V| |E|^2); this is the first polynomial time algorithm that checks vulnerability for general directed multigraphs. The resulting algorithm also contributes to another well known problem, i.e. the directed subgraph homeomorphism problem without node mapping, by providing another pattern graph for which a polynomial time algorithm exists.

cs.DS↗

arXiv2016

Graph Theoretic Investigations on Inefficiencies in Network Models

We consider network models where information items flow %are sent from a source to a sink node. We start with a model where routing is constrained by energy available on nodes in finite supply (like in Smartdust) and efficiency is related to energy consumption. We characterize graph topologies ensuring that every saturating flow under every energy-to-node assignment is maximum and provide a polynomial-time algorithm for checking this property. We then consider the standard flow networks with capacity on edges, where again efficiency is related to maximality of saturating flows, and a traffic model for selfish routing, where efficiency is related to latency at a Wardrop equilibrium. Finally, we show that all these forms of inefficiency yield different classes of graphs (apart from the acyclic case, where the last two forms generate the same class). Interestingly, in all cases inefficient graphs can be made efficient by removing edges; this resembles a well-known phenomenon, called Braess's paradox.

cs.DM↗