Minimizing Sign Changes Rowwise: Consecutive Ones Property and Beyond

Fortin, D.; Tseveendorj, Ider

doi:10.1007/978-3-319-12583-1_2

Cited by 2 publications

(2 citation statements)

References 17 publications

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“…An approximate solution is reached using a relaxation of this optimization problem. Finally, [39,19] study related problems in the special case of {0, 1}-valued matrices.…”

Section: Seriationmentioning

confidence: 99%

Reconstruction of line-embeddings of graphons

Janssen

Smith

2022

Electron. J. Statist.

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Consider a random graph process with n vertices corresponding to points v i i.i.d.∼ Unif[0, 1] embedded randomly in the interval, and where edges are inserted between v i , v j independently with probability given by the graphon w(v i , v j ) ∈ [0, 1]. Following [11], we call a graphon w diagonally increasing if, for each x, w(x, y) decreases as y moves away from x. We call a permutation σ ∈ Sn an ordering of these vertices if v σ(i) < v σ(j) for all i < j, and ask: how can we accurately estimate σ from an observed graph? We present a randomized algorithm with output σ that, for a large class of graphons, achieves error max 1≤i≤n |σ(i) − σ(i)| = Õ( √ n) with high probability; we also show that this is the best-possible convergence rate for a large class of algorithms and proof strategies. Under an additional assumption that is satisfied by some popular graphon models, we break this "barrier" at √ n and obtain the vastly better rate Õ(n ) for any > 0. These improved seriation bounds can be combined with previous work to give more efficient and accurate algorithms for related tasks, including estimating diagonally increasing graphons [20,21] and testing whether a graphon is diagonally increasing [11].

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“…An approximate solution is reached using a relaxation of this optimization problem. Finally, [39,19] study related problems in the special case of {0, 1}-valued matrices.…”

Section: Seriationmentioning

confidence: 99%

Reconstruction of line-embeddings of graphons

Janssen

Smith

2022

Electron. J. Statist.

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show abstract

“…An approximate solution is reached using a relaxation of this optimization problem. Finally, [Vuo10,FT15] study related problems in the special case of {0, 1}-valued matrices.…”

Section: Introductionmentioning

confidence: 99%

Reconstruction of Line-Embeddings of Graphons

Janssen¹,

Smith²

2020

Preprint

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Consider a random graph process with n vertices corresponding to points v i i.i.d. ∼Unif[0, 1] embedded randomly in the interval, and where edges are inserted between v i , v j independently with probability given by the graphon w(v i , v j ) ∈ [0, 1]. Following [CGH + 15], we call a graphon w diagonally increasing if, for each x, w(x, y) decreases as y moves away from x. We call a permutation σ ∈ S n an ordering of these vertices if v σ(i) < v σ(j) for all i < j, and ask: how can we accurately estimate σ from an observed graph? We present a randomized algorithm with output σ that, for a large class of graphons, achieves error max 1≤i≤n |σ(i) − σ(i)| = O * ( √ n) with high probability; we also show that this is the bestpossible convergence rate for a large class of algorithms and proof strategies. Under an additional assumption that is satisfied by some popular graphon models, we break this "barrier" at √ n and obtain the vastly better rate O * (n ǫ ) for any ǫ > 0. These improved seriation bounds can be combined with previous work to give more efficient and accurate algorithms for related tasks, including estimating diagonally increasing graphons [GLZ15, GJ20] and testing whether a graphon is diagonally increasing [CGH + 15].

show abstract

Minimizing Sign Changes Rowwise: Consecutive Ones Property and Beyond

Cited by 2 publications

References 17 publications

Reconstruction of line-embeddings of graphons

Reconstruction of line-embeddings of graphons

Reconstruction of Line-Embeddings of Graphons

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