8 Search Results for "Cheung, Yun Kuen"

Document
DOI: 10.4230/LIPIcs.ESA.2025.10
Connected Partitions via Connected Dominating Sets

Authors: Aikaterini Niklanovits, Kirill Simonov, Shaily Verma, and Ziena Zeif

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
The classical theorem due to Győri and Lovász states that any k-connected graph G admits a partition into k connected subgraphs, where each subgraph has a prescribed size and contains a prescribed vertex, as long as the total size of target subgraphs is equal to the size of G. However, this result is notoriously evasive in terms of efficient constructions, and it is still unknown whether such a partition can be computed in polynomial time, even for k = 5. We make progress towards an efficient constructive version of the Győri-Lovász theorem by considering a natural strengthening of the k-connectivity requirement. Specifically, we show that the desired connected partition can be found in polynomial time, if G contains k disjoint connected dominating sets. As a consequence of this result, we give several efficient approximate and exact constructive versions of the original Győri-Lovász theorem: - On general graphs, a Győri-Lovász partition with k parts can be computed in polynomial time when the input graph has connectivity Ω(k ⋅ log² n); - On convex bipartite graphs, connectivity of 4k is sufficient; - On biconvex graphs and interval graphs, connectivity of k is sufficient, meaning that our algorithm gives a "true" constructive version of the theorem on these graph classes.
Cite as

Aikaterini Niklanovits, Kirill Simonov, Shaily Verma, and Ziena Zeif. Connected Partitions via Connected Dominating Sets. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 10:1-10:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{niklanovits_et_al:LIPIcs.ESA.2025.10,
  author =	{Niklanovits, Aikaterini and Simonov, Kirill and Verma, Shaily and Zeif, Ziena},
  title =	{{Connected Partitions via Connected Dominating Sets}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{10:1--10:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.10},
  URN =		{urn:nbn:de:0030-drops-244785},
  doi =		{10.4230/LIPIcs.ESA.2025.10},
  annote =	{Keywords: Gy\H{o}ri-Lov\'{a}sz theorem, connected dominating sets, graph classes}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.65
Parameterized Spanning Tree Congestion

Authors: Michael Lampis, Valia Mitsou, Edouard Nemery, Yota Otachi, Manolis Vasilakis, and Daniel Vaz

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
In this paper we study the Spanning Tree Congestion problem, where we are given an undirected graph G = (V,E) and are asked to find a spanning tree T of minimum maximum congestion. Here, the congestion of an edge e ∈ T is the number of edges uv ∈ E such that the (unique) path from u to v in T traverses e. We consider this well-studied NP-hard problem from the point of view of (structural) parameterized complexity and obtain the following results: - We resolve a natural open problem by showing that Spanning Tree Congestion is not FPT parameterized by treewidth (under standard assumptions). More strongly, we present a generic reduction which applies to (almost) any parameter of the form "vertex-deletion distance to class 𝒞", thus obtaining W[1]-hardness for more restricted parameters, including tree-depth plus feedback vertex set, or incomparable to treewidth, such as twin cover. Via a slight tweak of the same reduction we also show that the problem is NP-complete on graphs of modular-width 4. - Even though it is known that Spanning Tree Congestion remains NP-hard on instances with only one vertex of unbounded degree, it is currently open whether the problem remains hard on bounded-degree graphs. We resolve this question by showing NP-hardness on graphs of maximum degree 8. - Complementing the problem’s W[1]-hardness for treewidth, we formulate an algorithm that runs in time roughly {(k+w)}^{𝒪(w)}, where k is the desired congestion and w the treewidth, improving a previous argument for parameter k+w that was based on Courcelle’s theorem. This explicit algorithm pays off in two ways: it allows us to obtain an FPT approximation scheme for parameter treewidth, that is, a (1+ε)-approximation running in time roughly {(w/ε)}^{𝒪(w)}; and it leads to an exact FPT algorithm for parameter clique-width+k via a Win/Win argument. - Finally, motivated by the problem’s hardness for most standard structural parameters, we present FPT algorithms for several more restricted cases, namely, for the parameters vertex-deletion distance to clique; vertex integrity; and feedback edge set, in the latter case also achieving a single-exponential running time dependence on the parameter.
Cite as

Michael Lampis, Valia Mitsou, Edouard Nemery, Yota Otachi, Manolis Vasilakis, and Daniel Vaz. Parameterized Spanning Tree Congestion. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 65:1-65:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lampis_et_al:LIPIcs.MFCS.2025.65,
  author =	{Lampis, Michael and Mitsou, Valia and Nemery, Edouard and Otachi, Yota and Vasilakis, Manolis and Vaz, Daniel},
  title =	{{Parameterized Spanning Tree Congestion}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{65:1--65:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.65},
  URN =		{urn:nbn:de:0030-drops-241724},
  doi =		{10.4230/LIPIcs.MFCS.2025.65},
  annote =	{Keywords: Parameterized Complexity, Treewidth, Graph Width Parameters}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.49
On Sparse Covers of Minor Free Graphs, Low Dimensional Metric Embeddings, and Other Applications

Authors: Arnold Filtser

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
Given a metric space (X,d_X), a (β,s,Δ)-sparse cover is a collection of clusters 𝒞 ⊆ P(X) with diameter at most Δ, such that for every point x ∈ X, the ball B_X(x,Δ/β) is fully contained in some cluster C ∈ 𝒞, and x belongs to at most s clusters in 𝒞. Our main contribution is to show that the shortest path metric of every K_r-minor free graphs admits (O(r),O(r²),Δ)-sparse cover, and for every ε > 0, (4+ε,O(1/ε)^r,Δ)-sparse cover (for arbitrary Δ > 0). We then use this sparse cover to show that every K_r-minor free graph embeds into 𝓁_∞^{Õ(1/ε)^{r+1}⋅log n} with distortion 3+ε (resp. into 𝓁_∞^{Õ(r²)⋅log n} with distortion O(r)). Further, among other applications, this sparse cover immediately implies an algorithm for the oblivious buy-at-bulk problem in fixed minor free graphs with the tight approximation factor O(log n) (previously nothing beyond general graphs was known).
Cite as

Arnold Filtser. On Sparse Covers of Minor Free Graphs, Low Dimensional Metric Embeddings, and Other Applications. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 49:1-49:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{filtser:LIPIcs.SoCG.2025.49,
  author =	{Filtser, Arnold},
  title =	{{On Sparse Covers of Minor Free Graphs, Low Dimensional Metric Embeddings, and Other Applications}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{49:1--49:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.49},
  URN =		{urn:nbn:de:0030-drops-232015},
  doi =		{10.4230/LIPIcs.SoCG.2025.49},
  annote =	{Keywords: Sparse cover, minor free graphs, metric embeddings, 𝓁\underline∞, oblivious buy-at-bulk}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.63
Approximation of Spanning Tree Congestion Using Hereditary Bisection

Authors: Petr Kolman

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

Abstract
The Spanning Tree Congestion (STC) problem is the following NP-hard problem: given a graph G, construct a spanning tree T of G minimizing its maximum edge congestion where the congestion of an edge e ∈ T is the number of edges uv in G such that the unique path between u and v in T passes through e; the optimal value for a given graph G is denoted STC(G). It is known that every spanning tree is an n/2-approximation for the STC problem. A long-standing problem is to design a better approximation algorithm. Our contribution towards this goal is an 𝒪(Δ⋅log^{3/2}n)-approximation algorithm where Δ is the maximum degree in G and n the number of vertices. For graphs with a maximum degree bounded by a polylog of the number of vertices, this is an exponential improvement over the previous best approximation. Our main tool for the algorithm is a new lower bound on the spanning tree congestion which is of independent interest. Denoting by hb(G) the hereditary bisection of G which is the maximum bisection width over all subgraphs of G, we prove that for every graph G, STC(G) ≥ Ω(hb(G)/Δ).
Cite as

Petr Kolman. Approximation of Spanning Tree Congestion Using Hereditary Bisection. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 63:1-63:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kolman:LIPIcs.STACS.2025.63,
  author =	{Kolman, Petr},
  title =	{{Approximation of Spanning Tree Congestion Using Hereditary Bisection}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{63:1--63:6},
  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.2025.63},
  URN =		{urn:nbn:de:0030-drops-228880},
  doi =		{10.4230/LIPIcs.STACS.2025.63},
  annote =	{Keywords: Spanning Tree Congestion, Bisection, Expansion, Divide and Conquer}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2018.25
On Fair Division for Indivisible Items

Authors: Bhaskar Ray Chaudhury, Yun Kuen Cheung, Jugal Garg, Naveen Garg, Martin Hoefer, and Kurt Mehlhorn

Published in: LIPIcs, Volume 122, 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)

Abstract
We consider the task of assigning indivisible goods to a set of agents in a fair manner. Our notion of fairness is Nash social welfare, i.e., the goal is to maximize the geometric mean of the utilities of the agents. Each good comes in multiple items or copies, and the utility of an agent diminishes as it receives more items of the same good. The utility of a bundle of items for an agent is the sum of the utilities of the items in the bundle. Each agent has a utility cap beyond which he does not value additional items. We give a polynomial time approximation algorithm that maximizes Nash social welfare up to a factor of e^{1/{e}} ~~ 1.445. The computed allocation is Pareto-optimal and approximates envy-freeness up to one item up to a factor of 2 + epsilon.
Cite as

Bhaskar Ray Chaudhury, Yun Kuen Cheung, Jugal Garg, Naveen Garg, Martin Hoefer, and Kurt Mehlhorn. On Fair Division for Indivisible Items. In 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 122, pp. 25:1-25:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{chaudhury_et_al:LIPIcs.FSTTCS.2018.25,
  author =	{Chaudhury, Bhaskar Ray and Cheung, Yun Kuen and Garg, Jugal and Garg, Naveen and Hoefer, Martin and Mehlhorn, Kurt},
  title =	{{On Fair Division for Indivisible Items}},
  booktitle =	{38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)},
  pages =	{25:1--25:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-093-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{122},
  editor =	{Ganguly, Sumit and Pandya, Paritosh},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2018.25},
  URN =		{urn:nbn:de:0030-drops-99242},
  doi =		{10.4230/LIPIcs.FSTTCS.2018.25},
  annote =	{Keywords: Fair Division, Indivisible Goods, Envy-Free}
}
Document
DOI: 10.4230/LIPIcs.ESA.2018.18
Amortized Analysis of Asynchronous Price Dynamics

Authors: Yun Kuen Cheung and Richard Cole

Published in: LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018)

Abstract
We extend a recently developed framework for analyzing asynchronous coordinate descent algorithms to show that an asynchronous version of tatonnement, a fundamental price dynamic widely studied in general equilibrium theory, converges toward a market equilibrium for Fisher markets with CES utilities or Leontief utilities, for which tatonnement is equivalent to coordinate descent.
Cite as

Yun Kuen Cheung and Richard Cole. Amortized Analysis of Asynchronous Price Dynamics. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 18:1-18:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{cheung_et_al:LIPIcs.ESA.2018.18,
  author =	{Cheung, Yun Kuen and Cole, Richard},
  title =	{{Amortized Analysis of Asynchronous Price Dynamics}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{18:1--18:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Azar, Yossi and Bast, Hannah and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2018.18},
  URN =		{urn:nbn:de:0030-drops-94812},
  doi =		{10.4230/LIPIcs.ESA.2018.18},
  annote =	{Keywords: Asynchronous Tatonnement, Fisher Market, Market Equilibrium, Amortized Analysis}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.32
Spanning Tree Congestion and Computation of Generalized Györi-Lovász Partition

Authors: L. Sunil Chandran, Yun Kuen Cheung, and Davis Issac

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
We study a natural problem in graph sparsification, the Spanning Tree Congestion (STC) problem. Informally, it seeks a spanning tree with no tree-edge routing too many of the original edges. For any general connected graph with n vertices and m edges, we show that its STC is at most O(sqrt{mn}), which is asymptotically optimal since we also demonstrate graphs with STC at least Omega(sqrt{mn}). We present a polynomial-time algorithm which computes a spanning tree with congestion O(sqrt{mn}* log n). We also present another algorithm for computing a spanning tree with congestion O(sqrt{mn}); this algorithm runs in sub-exponential time when m = omega(n log^2 n). For achieving the above results, an important intermediate theorem is generalized Györi-Lovász theorem. Chen et al. [Jiangzhuo Chen et al., 2007] gave a non-constructive proof. We give the first elementary and constructive proof with a local search algorithm of running time O^*(4^n). We discuss some consequences of the theorem concerning graph partitioning, which might be of independent interest. We also show that for any graph which satisfies certain expanding properties, its STC is at most O(n), and a corresponding spanning tree can be computed in polynomial time. We then use this to show that a random graph has STC Theta(n) with high probability.
Cite as

L. Sunil Chandran, Yun Kuen Cheung, and Davis Issac. Spanning Tree Congestion and Computation of Generalized Györi-Lovász Partition. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 32:1-32:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{chandran_et_al:LIPIcs.ICALP.2018.32,
  author =	{Chandran, L. Sunil and Cheung, Yun Kuen and Issac, Davis},
  title =	{{Spanning Tree Congestion and Computation of Generalized Gy\"{o}ri-Lov\'{a}sz Partition}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{32:1--32:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.32},
  URN =		{urn:nbn:de:0030-drops-90361},
  doi =		{10.4230/LIPIcs.ICALP.2018.32},
  annote =	{Keywords: Spanning Tree Congestion, Graph Sparsification, Graph Partitioning, Min-Max Graph Partitioning, k-Vertex-Connected Graphs, Gy\"{o}ri-Lov\'{a}sz Theorem}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2016.131
Graph Minors for Preserving Terminal Distances Approximately - Lower and Upper Bounds

Authors: Yun Kuen Cheung, Gramoz Goranci, and Monika Henzinger

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract
Given a graph where vertices are partitioned into k terminals and non-terminals, the goal is to compress the graph (i.e., reduce the number of non-terminals) using minor operations while preserving terminal distances approximately. The distortion of a compressed graph is the maximum multiplicative blow-up of distances between all pairs of terminals. We study the trade-off between the number of non-terminals and the distortion. This problem generalizes the Steiner Point Removal (SPR) problem, in which all non-terminals must be removed. We introduce a novel black-box reduction to convert any lower bound on distortion for the SPR problem into a super-linear lower bound on the number of non-terminals, with the same distortion, for our problem. This allows us to show that there exist graphs such that every minor with distortion less than 2 / 2.5 / 3 must have Omega(k^2) / Omega(k^{5/4}) / Omega(k^{6/5}) non-terminals, plus more trade-offs in between. The black-box reduction has an interesting consequence: if the tight lower bound on distortion for the SPR problem is super-constant, then allowing any O(k) non-terminals will not help improving the lower bound to a constant. We also build on the existing results on spanners, distance oracles and connected 0-extensions to show a number of upper bounds for general graphs, planar graphs, graphs that exclude a fixed minor and bounded treewidth graphs. Among others, we show that any graph admits a minor with O(log k) distortion and O(k^2) non-terminals, and any planar graph admits a minor with 1 + epsilon distortion and ~O((k/epsilon)^2) non-terminals.
Cite as

Yun Kuen Cheung, Gramoz Goranci, and Monika Henzinger. Graph Minors for Preserving Terminal Distances Approximately - Lower and Upper Bounds. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 131:1-131:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{cheung_et_al:LIPIcs.ICALP.2016.131,
  author =	{Cheung, Yun Kuen and Goranci, Gramoz and Henzinger, Monika},
  title =	{{Graph Minors for Preserving Terminal Distances Approximately - Lower and Upper Bounds}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{131:1--131:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.131},
  URN =		{urn:nbn:de:0030-drops-62675},
  doi =		{10.4230/LIPIcs.ICALP.2016.131},
  annote =	{Keywords: Distance Approximating Minor, Graph Minor, Graph Compression, Vertex Sparsification, Metric Embedding}
}
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