10 Search Results for "Kang, Mihyun"

Document
DOI: 10.4230/LIPIcs.DISC.2025.40
On the Randomized Locality of Matching Problems in Regular Graphs

Authors: Seri Khoury, Manish Purohit, Aaron Schild, and Joshua R. Wang

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
The main goal in distributed symmetry-breaking is to understand the locality of problems: the radius of the neighborhood that a node must explore to determine its part of a global solution. In this work, we study the locality of matching problems in the family of regular graphs, which is one of the main benchmarks for establishing lower bounds on the locality of symmetry-breaking problems, as well as for obtaining classification results. Our main results are summarized as follows: 1) Approximate matching: We develop randomized algorithms to show that (1 + ε)-approximate matching in regular graphs is truly local, i.e., the locality depends only on ε and is independent of all other graph parameters. Furthermore, as long as the degree Δ is not very small (namely, as long as Δ ≥ poly(1/ε)), this dependence is only logarithmic in 1/ε. This stands in sharp contrast to maximal matching in regular graphs which requires some dependence on the number of nodes n or the degree Δ. 2) Maximal matching: Our techniques further allow us to establish a strong separation between the node-averaged complexity and worst-case complexity of maximal matching in regular graphs, by showing that the former is only O(1). Central to our main technical contribution is a novel martingale-based analysis for the ≈ 40-year-old algorithm by Luby. In particular, our analysis shows that applying one round of Luby’s algorithm on the line graph of a Δ-regular graph results in an almost Δ/2-regular graph.
Cite as

Seri Khoury, Manish Purohit, Aaron Schild, and Joshua R. Wang. On the Randomized Locality of Matching Problems in Regular Graphs. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 40:1-40:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{khoury_et_al:LIPIcs.DISC.2025.40,
  author =	{Khoury, Seri and Purohit, Manish and Schild, Aaron and Wang, Joshua R.},
  title =	{{On the Randomized Locality of Matching Problems in Regular Graphs}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{40:1--40:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.40},
  URN =		{urn:nbn:de:0030-drops-248570},
  doi =		{10.4230/LIPIcs.DISC.2025.40},
  annote =	{Keywords: regular graphs, maximum matching, augmenting paths, distributed algorithms, Luby’s algorithm, martingales}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.47
Belief Propagation Guided Decimation on Random k-XORSAT

Authors: Arnab Chatterjee, Amin Coja-Oghlan, Mihyun Kang, Lena Krieg, Maurice Rolvien, and Gregory B. Sorkin

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
We analyse the performance of Belief Propagation Guided Decimation, a physics-inspired message passing algorithm, on the random k-XORSAT problem. Specifically, we derive an explicit threshold up to which the algorithm succeeds with a strictly positive probability Ω(1) that we compute explicitly, but beyond which the algorithm with high probability fails to find a satisfying assignment. In addition, we analyse a thought experiment called the decimation process for which we identify a (non-) reconstruction and a condensation phase transition. The main results of the present work confirm physics predictions from [Ricci-Tersenghi and Semerjian: J. Stat. Mech. 2009] that link the phase transitions of the decimation process with the performance of the algorithm, and improve over partial results from a recent article [Yung: Proc. ICALP 2024].
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Arnab Chatterjee, Amin Coja-Oghlan, Mihyun Kang, Lena Krieg, Maurice Rolvien, and Gregory B. Sorkin. Belief Propagation Guided Decimation on Random k-XORSAT. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 47:1-47:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chatterjee_et_al:LIPIcs.ICALP.2025.47,
  author =	{Chatterjee, Arnab and Coja-Oghlan, Amin and Kang, Mihyun and Krieg, Lena and Rolvien, Maurice and Sorkin, Gregory B.},
  title =	{{Belief Propagation Guided Decimation on Random k-XORSAT}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{47:1--47:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.47},
  URN =		{urn:nbn:de:0030-drops-234248},
  doi =		{10.4230/LIPIcs.ICALP.2025.47},
  annote =	{Keywords: random k-XORSAT, belief propagation, decimation process, random matrices}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.46
Sampling Unlabeled Chordal Graphs in Expected Polynomial Time

Authors: Úrsula Hébert-Johnson and Daniel Lokshtanov

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
We design an algorithm that generates an n-vertex unlabeled chordal graph uniformly at random in expected polynomial time. Along the way, we develop the following two results: (1) an FPT algorithm for counting and sampling labeled chordal graphs with a given automorphism π, parameterized by the number of moved points of π, and (2) a proof that the probability that a random n-vertex labeled chordal graph has a given automorphism π ∈ S_n is at most 1/2^{c max{μ²,n}}, where μ is the number of moved points of π and c is a constant. Our algorithm for sampling unlabeled chordal graphs calls the aforementioned FPT algorithm as a black box with potentially large values of the parameter μ, but the probability of calling this algorithm with a large value of μ is exponentially small.
Cite as

Úrsula Hébert-Johnson and Daniel Lokshtanov. Sampling Unlabeled Chordal Graphs in Expected Polynomial Time. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 46:1-46:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hebertjohnson_et_al:LIPIcs.STACS.2025.46,
  author =	{H\'{e}bert-Johnson, \'{U}rsula and Lokshtanov, Daniel},
  title =	{{Sampling Unlabeled Chordal Graphs in Expected Polynomial Time}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{46:1--46:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.46},
  URN =		{urn:nbn:de:0030-drops-228726},
  doi =		{10.4230/LIPIcs.STACS.2025.46},
  annote =	{Keywords: Chordal graphs, graph sampling, graph counting, unlabeled graphs}
}
Document
DOI: 10.4230/LIPIcs.AofA.2020.13
Counting Cubic Maps with Large Genus

Authors: Zhicheng Gao and Mihyun Kang

Published in: LIPIcs, Volume 159, 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020)

Abstract
We derive an asymptotic expression for the number of cubic maps on orientable surfaces when the genus is proportional to the number of vertices. Let Σ_g denote the orientable surface of genus g and θ=g/n∈ (0,1/2). Given g,n∈ ℕ with g→ ∞ and n/2-g→ ∞ as n→ ∞, the number C_{n,g} of cubic maps on Σ_g with 2n vertices satisfies C_{n,g} ∼ (g!)² α(θ) β(θ)ⁿ γ(θ)^{2g}, as g→ ∞, where α(θ),β(θ),γ(θ) are differentiable functions in (0,1/2). This also leads to the asymptotic number of triangulations (as the dual of cubic maps) with large genus. When g/n lies in a closed subinterval of (0,1/2), the asymptotic formula can be obtained using a local limit theorem. The saddle-point method is applied when g/n→ 0 or g/n→ 1/2.
Cite as

Zhicheng Gao and Mihyun Kang. Counting Cubic Maps with Large Genus. In 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 159, pp. 13:1-13:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{gao_et_al:LIPIcs.AofA.2020.13,
  author =	{Gao, Zhicheng and Kang, Mihyun},
  title =	{{Counting Cubic Maps with Large Genus}},
  booktitle =	{31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020)},
  pages =	{13:1--13:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-147-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{159},
  editor =	{Drmota, Michael and Heuberger, Clemens},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2020.13},
  URN =		{urn:nbn:de:0030-drops-120437},
  doi =		{10.4230/LIPIcs.AofA.2020.13},
  annote =	{Keywords: cubic maps, triangulations, cubic graphs on surfaces, generating functions, asymptotic enumeration, local limit theorem, saddle-point method}
}
Document
DOI: 10.4230/LIPIcs.AofA.2020.18
The Giant Component and 2-Core in Sparse Random Outerplanar Graphs

Authors: Mihyun Kang and Michael Missethan

Published in: LIPIcs, Volume 159, 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020)

Abstract
Let A(n,m) be a graph chosen uniformly at random from the class of all vertex-labelled outerplanar graphs with n vertices and m edges. We consider A(n,m) in the sparse regime when m=n/2+s for s=o(n). We show that with high probability the giant component in A(n,m) emerges at m=n/2+O (n^{2/3}) and determine the typical order of the 2-core. In addition, we prove that if s=ω(n^{2/3}), with high probability every edge in A(n,m) belongs to at most one cycle.
Cite as

Mihyun Kang and Michael Missethan. The Giant Component and 2-Core in Sparse Random Outerplanar Graphs. In 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 159, pp. 18:1-18:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{kang_et_al:LIPIcs.AofA.2020.18,
  author =	{Kang, Mihyun and Missethan, Michael},
  title =	{{The Giant Component and 2-Core in Sparse Random Outerplanar Graphs}},
  booktitle =	{31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020)},
  pages =	{18:1--18:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-147-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{159},
  editor =	{Drmota, Michael and Heuberger, Clemens},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2020.18},
  URN =		{urn:nbn:de:0030-drops-120488},
  doi =		{10.4230/LIPIcs.AofA.2020.18},
  annote =	{Keywords: giant component, core, outerplanar graphs, singularity analysis}
}
Document
Keynote Speakers
DOI: 10.4230/LIPIcs.AofA.2018.7
Vanishing of Cohomology Groups of Random Simplicial Complexes (Keynote Speakers)

Authors: Oliver Cooley, Nicola Del Giudice, Mihyun Kang, and Philipp Sprüssel

Published in: LIPIcs, Volume 110, 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)

Abstract
We consider k-dimensional random simplicial complexes that are generated from the binomial random (k+1)-uniform hypergraph by taking the downward-closure, where k >= 2. For each 1 <= j <= k-1, we determine when all cohomology groups with coefficients in F_2 from dimension one up to j vanish and the zero-th cohomology group is isomorphic to F_2. This property is not monotone, but nevertheless we show that it has a single sharp threshold. Moreover, we prove a hitting time result, relating the vanishing of these cohomology groups to the disappearance of the last minimal obstruction. Furthermore, we study the asymptotic distribution of the dimension of the j-th cohomology group inside the critical window. As a corollary, we deduce a hitting time result for a different model of random simplicial complexes introduced in [Linial and Meshulam, Combinatorica, 2006], a result which has only been known for dimension two [Kahle and Pittel, Random Structures Algorithms, 2016].
Cite as

Oliver Cooley, Nicola Del Giudice, Mihyun Kang, and Philipp Sprüssel. Vanishing of Cohomology Groups of Random Simplicial Complexes (Keynote Speakers). In 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 110, pp. 7:1-7:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{cooley_et_al:LIPIcs.AofA.2018.7,
  author =	{Cooley, Oliver and Del Giudice, Nicola and Kang, Mihyun and Spr\"{u}ssel, Philipp},
  title =	{{Vanishing of Cohomology Groups of Random Simplicial Complexes}},
  booktitle =	{29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)},
  pages =	{7:1--7:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-078-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{110},
  editor =	{Fill, James Allen and Ward, Mark Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2018.7},
  URN =		{urn:nbn:de:0030-drops-89006},
  doi =		{10.4230/LIPIcs.AofA.2018.7},
  annote =	{Keywords: Random hypergraphs, random simplicial complexes, sharp threshold, hitting time, connectedness}
}
Document
DOI: 10.4230/LIPIcs.AofA.2018.17
The Genus of the Erdös-Rényi Random Graph and the Fragile Genus Property

Authors: Chris Dowden, Mihyun Kang, and Michael Krivelevich

Published in: LIPIcs, Volume 110, 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)

Abstract
We investigate the genus g(n,m) of the Erdös-Rényi random graph G(n,m), providing a thorough description of how this relates to the function m=m(n), and finding that there is different behaviour depending on which `region' m falls into. Existing results are known for when m is at most n/(2) + O(n^{2/3}) and when m is at least omega (n^{1+1/(j)}) for j in N, and so we focus on intermediate cases. In particular, we show that g(n,m) = (1+o(1)) m/(2) whp (with high probability) when n << m = n^{1+o(1)}; that g(n,m) = (1+o(1)) mu (lambda) m whp for a given function mu (lambda) when m ~ lambda n for lambda > 1/2; and that g(n,m) = (1+o(1)) (8s^3)/(3n^2) whp when m = n/(2) + s for n^(2/3) << s << n. We then also show that the genus of fixed graphs can increase dramatically if a small number of random edges are added. Given any connected graph with bounded maximum degree, we find that the addition of epsilon n edges will whp result in a graph with genus Omega (n), even when epsilon is an arbitrarily small constant! We thus call this the `fragile genus' property.
Cite as

Chris Dowden, Mihyun Kang, and Michael Krivelevich. The Genus of the Erdös-Rényi Random Graph and the Fragile Genus Property. In 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 110, pp. 17:1-17:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{dowden_et_al:LIPIcs.AofA.2018.17,
  author =	{Dowden, Chris and Kang, Mihyun and Krivelevich, Michael},
  title =	{{The Genus of the Erd\"{o}s-R\'{e}nyi Random Graph and the Fragile Genus Property}},
  booktitle =	{29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)},
  pages =	{17:1--17:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-078-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{110},
  editor =	{Fill, James Allen and Ward, Mark Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2018.17},
  URN =		{urn:nbn:de:0030-drops-89100},
  doi =		{10.4230/LIPIcs.AofA.2018.17},
  annote =	{Keywords: Random graphs, Genus, Fragile genus}
}
Document
DOI: 10.4230/LIPIcs.AofA.2018.29
Asymptotic Expansions for Sub-Critical Lagrangean Forms

Authors: Hsien-Kuei Hwang, Mihyun Kang, and Guan-Huei Duh

Published in: LIPIcs, Volume 110, 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)

Abstract
Asymptotic expansions for the Taylor coefficients of the Lagrangean form phi(z)=zf(phi(z)) are examined with a focus on the calculations of the asymptotic coefficients. The expansions are simple and useful, and we discuss their use in some enumerating sequences in trees, lattice paths and planar maps.
Cite as

Hsien-Kuei Hwang, Mihyun Kang, and Guan-Huei Duh. Asymptotic Expansions for Sub-Critical Lagrangean Forms. In 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 110, pp. 29:1-29:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{hwang_et_al:LIPIcs.AofA.2018.29,
  author =	{Hwang, Hsien-Kuei and Kang, Mihyun and Duh, Guan-Huei},
  title =	{{Asymptotic Expansions for Sub-Critical Lagrangean Forms}},
  booktitle =	{29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)},
  pages =	{29:1--29:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-078-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{110},
  editor =	{Fill, James Allen and Ward, Mark Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2018.29},
  URN =		{urn:nbn:de:0030-drops-89224},
  doi =		{10.4230/LIPIcs.AofA.2018.29},
  annote =	{Keywords: asymptotic expansions, Lagrangean forms, saddle-point method, singularity analysis, maps}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2017.40
Charting the Replica Symmetric Phase

Authors: Amin Coja-Oghlan, Charilaos Efthymiou, Nor Jaafari, Mihyun Kang, and Tobias Kapetanopoulos

Published in: LIPIcs, Volume 81, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)

Abstract
Random graph models and associated inference problems such as the stochastic block model play an eminent role in computer science, discrete mathematics and statistics. Based on non-rigorous arguments physicists predicted the existence of a generic phase transition that separates a "replica symmetric phase" where statistical inference is impossible from a phase where the detection of the "ground truth" is information-theoretically possible. In this paper we prove a contiguity result that shows that detectability is indeed impossible within the replica-symmetric phase for a broad class of models. In particular, this implies the detectability conjecture for the disassortative stochastic block model from [Decelle et al.: Phys Rev E 2011]. Additionally, we investigate key features of the replica symmetric phase such as the nature of point-to-set correlations (`reconstruction').
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Amin Coja-Oghlan, Charilaos Efthymiou, Nor Jaafari, Mihyun Kang, and Tobias Kapetanopoulos. Charting the Replica Symmetric Phase. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 81, pp. 40:1-40:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{cojaoghlan_et_al:LIPIcs.APPROX-RANDOM.2017.40,
  author =	{Coja-Oghlan, Amin and Efthymiou, Charilaos and Jaafari, Nor and Kang, Mihyun and Kapetanopoulos, Tobias},
  title =	{{Charting the Replica Symmetric Phase}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)},
  pages =	{40:1--40:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-044-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{81},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} D. P. and Williamson, David P. and Vempala, Santosh S.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2017.40},
  URN =		{urn:nbn:de:0030-drops-75895},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2017.40},
  annote =	{Keywords: Random factor graph, bounds for condensation phase transition, Potts antiferromagnet, diluted k-spin model, stochastic block model}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2015.710
The Minimum Bisection in the Planted Bisection Model

Authors: Amin Coja-Oghlan, Oliver Cooley, Mihyun Kang, and Kathrin Skubch

Published in: LIPIcs, Volume 40, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)

Abstract
In the planted bisection model a random graph G(n,p_+,p_-) with n vertices is created by partitioning the vertices randomly into two classes of equal size (up to plus or minus 1). Any two vertices that belong to the same class are linked by an edge with probability p_+ and any two that belong to different classes with probability (p_-) <(p_+) independently. The planted bisection model has been used extensively to benchmark graph partitioning algorithms. If (p_+)=2(d_+)/n and (p_-)=2(d_-)/n for numbers 0 <= (d_-) <(d_+) that remain fixed as n tends to infinity, then with high probability the "planted" bisection (the one used to construct the graph) will not be a minimum bisection. In this paper we derive an asymptotic formula for the minimum bisection width under the assumption that (d_+)-(d_-) > c * sqrt((d_+)ln(d_+)) for a certain constant c>0.
Cite as

Amin Coja-Oghlan, Oliver Cooley, Mihyun Kang, and Kathrin Skubch. The Minimum Bisection in the Planted Bisection Model. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 40, pp. 710-725, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{cojaoghlan_et_al:LIPIcs.APPROX-RANDOM.2015.710,
  author =	{Coja-Oghlan, Amin and Cooley, Oliver and Kang, Mihyun and Skubch, Kathrin},
  title =	{{The Minimum Bisection in the Planted Bisection Model}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)},
  pages =	{710--725},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-89-7},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{40},
  editor =	{Garg, Naveen and Jansen, Klaus and Rao, Anup and Rolim, Jos\'{e} D. P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2015.710},
  URN =		{urn:nbn:de:0030-drops-53315},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2015.710},
  annote =	{Keywords: Random graphs, minimum bisection, planted bisection, belief propagation.}
}
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