Flow Subgraphs and Flow Network Design under End-to-End Power Dissipation Constraints

TL;DR

This paper explores the structure of flow-supporting subgraphs in networks under power constraints, proposing algorithms to design sparse graphs that meet specific power dissipation and resistance criteria.

Contribution

It introduces the Resistor Gap Pruning heuristic for constructing sparse graphs that approximate desired effective resistance matrices under power constraints.

Findings

RGP produces sparse graphs closely matching target effective resistance matrices.

The heuristic demonstrates stable performance across various demand scenarios.

The approach effectively addresses inverse effective resistance problems in network design.

Abstract

We investigate how the underlying graph of a network supports a flow between a source node and a destination node and propose to compute the expected number of nodes and links that contribute to transferring items in random graphs. Since the transportation is associated with a \quotes{cost} or \quotes{power dissipation}, we further address how to construct a graph given predetermined end-to-end power dissipation, which can be reduced to the \quotes{inverse effective resistance problem} that asks for a weighted graph in which the effective resistance matrix equals a predetermined demand matrix. We propose a heuristic algorithm, \quotes{Resistor Gap Pruning} (RGP), which provides sparse graphs closely approximating the demand effective resistance and which shows stable performance across different demand scenarios.