Flow Subgraphs and Flow Network Design under End-to-End Power Dissipation Constraints
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 cost or power dissipation, we further address how to construct a graph given predetermined end-to-end power dissipation, which can be reduced to the 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, Resistor Gap Pruning (RGP), which provides sparse graphs closely approximating the demand effective resistance and which shows stable performance across different demand scenarios.
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