A note on using the resistance-distance matrix to solve Hamiltonian cycle problem

Ejov, Vladimir; Filar, Jerzy A.; Haythorpe, Michael; Roddick, John F.; Rossomakhine, Serguei

doi:10.1007/s10479-017-2571-7

Cited by 3 publications

(2 citation statements)

References 20 publications

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“…In Ejov et al (2019), the authors consider the entire set of resistance distances (again using unit values for edges), between any pair of nodes (not only leaves.) They show that using this metric is useful for discovering Hamiltonian cycles via algorithms for the Traveling Salesman problem.…”

Section: Introductionmentioning

confidence: 99%

Phylogenetic Networks as Circuits With Resistance Distance

Forcey

Scalzo

2020

Front. Genet.

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Phylogenetic networks are notoriously difficult to reconstruct. Here we suggest that it can be useful to view unknown genetic distance along edges in phylogenetic networks as analogous to unknown resistance in electric circuits. This resistance distance, well-known in graph theory, turns out to have nice mathematical properties which allow the precise reconstruction of networks. Specifically we show that the resistance distance for a weighted 1-nested network is Kalmanson, and that the unique associated circular split network fully represents the splits of the original phylogenetic network (or circuit). In fact, this full representation corresponds to a face of the balanced minimal evolution polytope for level-1 networks. Thus, the unweighted class of the original network can be reconstructed by either the greedy algorithm neighbor-net or by linear programming over a balanced minimal evolution polytope. We begin study of 2-nested networks with both minimum path and resistance distance, and include some counting results for 2-nested networks.

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Section: Introductionmentioning

confidence: 99%

Phylogenetic Networks as Circuits With Resistance Distance

Forcey

Scalzo

2020

Front. Genet.

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show abstract

“…In [9], the authors consider the entire set of resistance distances (again using unit values for edges), between any pair of nodes (not only leaves.) They show that using this metric is useful for discovering Hamiltonian cycles via algorithms for the Travelling Salesman problem.…”

Section: Introductionmentioning

confidence: 99%

Phylogenetic networks as circuits with resistance distance

Forcey¹,

Scalzo²

2020

Preprint

View full text Add to dashboard Cite

Phylogenetic networks are notoriously difficult to reconstruct. Here we suggest that it can be useful to view unknown genetic distance along edges in phylogenetic networks as analogous to unknown resistance in electric circuits. This resistance distance, well known in graph theory, turns out to have nice mathematical properties which allow the precise reconstruction of networks. Specifically we show that the resistance distance for a weighted 1-nested network is Kalmanson, and that the unique associated circular split network fully represents the splits of the original phylogenetic network (or circuit). In fact, this full representation corresponds to a face of the balanced minimal evolution polytope for level-1 networks. Thus the unweighted class of the original network can be reconstructed by either the greedy algorithm neighbor-net or by linear programming over a balanced minimal evolution polytope. We begin study of 2-nested networks with both minimum path and resistance distance, and include some counting results for 2-nested networks.

show abstract