Finding diverse ways to improve algebraic connectivity through multi-start optimization

Mackay, Sarah; Ponce, Colin; Osborn, Sarah; McGarry, Meghan

doi:10.1093/comnet/cnab005

Finding diverse ways to improve algebraic connectivity through multi-start optimization

Journal Article · 25 April 2021 · Journal of Complex Networks

DOI:https://doi.org/10.1093/comnet/cnab005· OSTI ID:1788312

Mackay, Sarah ^[1]; Ponce, Colin ^[1]; Osborn, Sarah ^[1]; McGarry, Meghan ^[2]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Global Security Computing

The algebraic connectivity, also known as the Fiedler value, is a spectral measure of network connectivity that can be increased through edge addition. We present an algorithm for producing many diverse ways to add a fixed number of edges to a network to achieve a near optimal Fiedler value. Previous Fielder value optimization algorithms (i.e. the greedy algorithm) output only one solution. Obtaining a single solution is rarely good enough for real-world network redesign problems, as practical constraints (political, physical or financial) may prevent implementation. Our algorithm takes a multi-start optimization approach, adding a random initial edge and then applies a greedy heuristic to improve the Fiedler value. The random choice moves us to a new region of the search space, enabling discovery of diverse solutions. Additionally, we present a Determinantal Point Process framework for quantifying diversity. We then apply a Markov chain Monte Carlo technique to sift through the large number of output solutions and locate a smaller, more manageable collection of highly diverse solutions that can be presented to network redesign engineers. We demonstrate the effectiveness of our algorithm on real-world graphs with varied structures.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1788312

Report Number(s):: LLNL-JRNL--810798; 1016974

Journal Information:: Journal of Complex Networks, Journal Name: Journal of Complex Networks Journal Issue: 1 Vol. 9; ISSN 2051-1310

Publisher:: Oxford University PressCopyright Statement

Country of Publication:: United States

Language:: English

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