35 Search Results for "Chalermsook, Parinya"

Document
DOI: 10.4230/LIPIcs.GD.2025.21
On Geometric Bipartite Graphs with Asymptotically Smallest Zarankiewicz Numbers

Authors: Parinya Chalermsook, Ly Orgo, and Minoo Zarsav

Published in: LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)

Abstract
This paper considers the Zarankiewicz problem in bipartite graphs with low-dimensional geometric representation (i.e., low Ferrers dimension). Let Z(n;k) be the maximum number of edges in a bipartite graph with n nodes and is free of a k-by-k biclique. Note that Z(n;k) ∈ Ω(nk) for all "natural" graph classes. Our first result reveals a separation between bipartite graphs of Ferrers dimension three and four: while we show that Z(n;k) ≤ 9n(k-1) for graphs of Ferrers dimension three, Z(n;k) ∈ Ω(n k ⋅ (log n)/(log log n)) for Ferrers dimension four graphs (Chan & Har-Peled, 2023) (Chazelle, 1990). To complement this, we derive a tight upper bound of 2n(k-1) for chordal bipartite graphs and 54n(k-1) for grid intersection graphs (GIG), a prominent graph class residing in four Ferrers dimensions and capturing planar bipartite graphs as well as bipartite intersection graphs of rectangles. Previously, the best-known bound for GIG was Z(n;k) ∈ O(2^{O(k)} n), implied by the results of Fox & Pach (2006) and Mustafa & Pach (2016). Our results advance and offer new insights into the interplay between Ferrers dimensions and extremal combinatorics.
Cite as

Parinya Chalermsook, Ly Orgo, and Minoo Zarsav. On Geometric Bipartite Graphs with Asymptotically Smallest Zarankiewicz Numbers. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 21:1-21:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{chalermsook_et_al:LIPIcs.GD.2025.21,
  author =	{Chalermsook, Parinya and Orgo, Ly and Zarsav, Minoo},
  title =	{{On Geometric Bipartite Graphs with Asymptotically Smallest Zarankiewicz Numbers}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{21:1--21:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.21},
  URN =		{urn:nbn:de:0030-drops-250074},
  doi =		{10.4230/LIPIcs.GD.2025.21},
  annote =	{Keywords: Bipartite graph classes, extremal graph theory, geometric intersection graphs, Zarankiewicz problem, bicliques}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.98
Fine-Grained Classification of Detecting Dominating Patterns

Authors: Jonathan Dransfeld, Marvin Künnemann, and Mirza Redzic

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

Abstract
We consider the following generalization of dominating sets: Let G be a host graph and P be a pattern graph P. A dominating P-pattern in G is a subset S of vertices in G that (1) forms a dominating set in G and (2) induces a subgraph isomorphic to P. The graph theory literature studies the properties of dominating P-patterns for various patterns P, including cliques, matchings, independent sets, cycles and paths. Previous work (Kunnemann, Redzic 2024) obtains algorithms and conditional lower bounds for detecting dominating P-patterns particularly for P being a k-clique, a k-independent set and a k-matching. Their results give conditionally tight lower bounds if k is sufficiently large (where the bound depends the matrix multiplication exponent ω). We ask: Can we obtain a classification of the fine-grained complexity for all patterns P? Indeed, we define a graph parameter ρ(P) such that if ω = 2, then (n^ρ(P) m^{(|V(P)|-ρ(P))/2})^{1±o(1)} is the optimal running time assuming the Orthogonal Vectors Hypothesis, for all patterns P except the triangle K₃. Here, the host graph G has n vertices and m = Θ(n^α) edges, where 1 ≤ α ≤ 2. The parameter ρ(P) is closely related (but sometimes different) to a parameter δ(P) = max_{S ⊆ V(P)} |S|-|N(S)| studied in (Alon 1981) to tightly quantify the maximum number of occurrences of induced subgraphs isomorphic to P. Our results stand in contrast to the lack of a full fine-grained classification of detecting an arbitrary (not necessarily dominating) induced P-pattern.
Cite as

Jonathan Dransfeld, Marvin Künnemann, and Mirza Redzic. Fine-Grained Classification of Detecting Dominating Patterns. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 98:1-98:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{dransfeld_et_al:LIPIcs.ESA.2025.98,
  author =	{Dransfeld, Jonathan and K\"{u}nnemann, Marvin and Redzic, Mirza},
  title =	{{Fine-Grained Classification of Detecting Dominating Patterns}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{98:1--98:15},
  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.2025.98},
  URN =		{urn:nbn:de:0030-drops-245679},
  doi =		{10.4230/LIPIcs.ESA.2025.98},
  annote =	{Keywords: fine-grained complexity theory, domination in graphs, subgraph isomorphism, classification theorem, parameterized algorithms}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.108
Deterministic Approximation Algorithm for Graph Burning

Authors: Matej Lieskovský

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

Abstract
Graph Burning models a contagion spreading in a network as a process such that in each step one node is infected and also the infection spreads to all neighbors of previously infected nodes. Formally, the burning number b(G) of a given graph G = (V,E), possibly with edge lengths, is the minimum number g such that there exists a sequence of nodes v₁,…,v_g satisfying the property that for each w ∈ V there exists i ∈ {1,…,g} so that the distance between w and v_i is at most g-i. We present an elegant deterministic 2.314-approximation algorithm for the Graph Burning problem on general graphs with arbitrary edge lengths. This algorithm matches the approximation ratio of the previous randomized 2.314-approximation algorithm and improves on the previous deterministic 3-approximation algorithm.
Cite as

Matej Lieskovský. Deterministic Approximation Algorithm for Graph Burning. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 108:1-108:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{lieskovsky:LIPIcs.ESA.2025.108,
  author =	{Lieskovsk\'{y}, Matej},
  title =	{{Deterministic Approximation Algorithm for Graph Burning}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{108:1--108:7},
  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.2025.108},
  URN =		{urn:nbn:de:0030-drops-245775},
  doi =		{10.4230/LIPIcs.ESA.2025.108},
  annote =	{Keywords: Graph Algorithms, Approximation Algorithms, Graph Burning}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.83
Fault-Tolerant Matroid Bases

Authors: Matthias Bentert, Fedor V. Fomin, Petr A. Golovach, and Laure Morelle

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

Abstract
We investigate the problem of constructing fault-tolerant bases in matroids. Given a matroid ℳ and a redundancy parameter k, a k-fault-tolerant basis is a minimum-size set of elements such that, even after the removal of any k elements, the remaining subset still spans the entire ground set. Since matroids generalize linear independence across structures such as vector spaces, graphs, and set systems, this problem unifies and extends several fault-tolerant concepts appearing in prior research. Our main contribution is a fixed-parameter tractable (FPT) algorithm for the k-fault-tolerant basis problem, parameterized by both k and the rank r of the matroid. This two-variable parameterization by k + r is shown to be tight in the following sense. On the one hand, the problem is already NP-hard for k = 1. On the other hand, it is Para-NP-hard for r ≥ 3 and polynomial-time solvable for r ≤ 2.
Cite as

Matthias Bentert, Fedor V. Fomin, Petr A. Golovach, and Laure Morelle. Fault-Tolerant Matroid Bases. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 83:1-83:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{bentert_et_al:LIPIcs.ESA.2025.83,
  author =	{Bentert, Matthias and Fomin, Fedor V. and Golovach, Petr A. and Morelle, Laure},
  title =	{{Fault-Tolerant Matroid Bases}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{83:1--83:14},
  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.2025.83},
  URN =		{urn:nbn:de:0030-drops-245511},
  doi =		{10.4230/LIPIcs.ESA.2025.83},
  annote =	{Keywords: Parameterized Complexity, matroids, robust bases}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.2
Covering Simple Orthogonal Polygons with Rectangles

Authors: Aniket Basu Roy

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
We study the problem of Covering Orthogonal Polygons with Rectangles, focusing on three variants: covering the interior, the boundary, and the corners. While previous work provided constant-factor approximation algorithms for these problems, significant improvements had not been achieved for over two decades. The main contribution of this work is the development of a Polynomial Time Approximation Scheme (PTAS) for both the Boundary Cover and Corner Cover problems on simple polygons, using a local search algorithm. Our work advances the state of the art, improving upon the previous best-known 4-approximation for the Boundary Cover and 2-approximation for the Corner Cover problems. The technical core of our work lies in proving the existence of planar support graphs for certain geometric hypergraphs defined by the polygon and its containment-maximal rectangles. This structural insight enables the application of the local search framework to achieve the PTAS results. We also demonstrate the limitations of this approach by constructing instances where local search fails for the Interior Cover and certain dual problems, such as the Maximum Antirectangle and Hitting Set problems. Additionally, the methods yield a PTAS for a special case of the Discrete Independent Set problem for rectangles. These results not only settle longstanding open questions but also introduce new techniques that may be of independent interest within computational geometry.
Cite as

Aniket Basu Roy. Covering Simple Orthogonal Polygons with Rectangles. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 2:1-2:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{basuroy:LIPIcs.APPROX/RANDOM.2025.2,
  author =	{Basu Roy, Aniket},
  title =	{{Covering Simple Orthogonal Polygons with Rectangles}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{2:1--2:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.2},
  URN =		{urn:nbn:de:0030-drops-243686},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.2},
  annote =	{Keywords: Polygon Covering, Approximation Algorithms, Orthogonal Polygons, Rectangles, Local Search, Planar Supports}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.11
On Finding Randomly Planted Cliques in Arbitrary Graphs

Authors: Francesco Agrimonti, Marco Bressan, and Tommaso d'Orsi

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
We study a planted clique model introduced by Feige [Uriel Feige, 2021] where a complete graph of size c⋅ n is planted uniformly at random in an arbitrary n-vertex graph. We give a simple deterministic algorithm that, in almost linear time, recovers a clique of size (c/3)^O(1/c) ⋅ n as long as the original graph has maximum degree at most (1-p)n for some fixed p > 0. The proof hinges on showing that the degrees of the final graph are correlated with the planted clique, in a way similar to (but more intricate than) the classical G(n,1/2)+K_√n planted clique model. Our algorithm suggests a separation from the worst-case model, where, assuming the Unique Games Conjecture, no polynomial algorithm can find cliques of size Ω(n) for every fixed c > 0, even if the input graph has maximum degree (1-p)n. Our techniques extend beyond the planted clique model. For example, when the planted graph is a balanced biclique, we recover a balanced biclique of size larger than the best guarantees known for the worst case.
Cite as

Francesco Agrimonti, Marco Bressan, and Tommaso d'Orsi. On Finding Randomly Planted Cliques in Arbitrary Graphs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 11:1-11:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{agrimonti_et_al:LIPIcs.APPROX/RANDOM.2025.11,
  author =	{Agrimonti, Francesco and Bressan, Marco and d'Orsi, Tommaso},
  title =	{{On Finding Randomly Planted Cliques in Arbitrary Graphs}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{11:1--11:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.11},
  URN =		{urn:nbn:de:0030-drops-243774},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.11},
  annote =	{Keywords: Computational Complexity, Planted Clique, Semi-random, Unique Games Conjecture, Approximation Algorithms}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.16
An Improved Guillotine Cut for Squares

Authors: Parinya Chalermsook, Axel Kugelmann, Ly Orgo, Sumedha Uniyal, and Minoo Zarsav

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
Given a set of n non-overlapping geometric objects, can we separate a constant fraction of them using straight-line cuts that extend from edge to edge? In 1996, Urrutia posed this question for compact convex objects. Pach and Tardos later refuted it for general line segments by constructing a family where any separable subfamily has size at most O (n^{log₃ 2}). However, for axis-parallel rectangles, they provided positive evidence, showing that an Ω(1/log n)-fraction can be separated. This problem naturally arises in geometric approximation algorithms. In particular, when restricting cuts to only orthogonal straight lines, known as a guillotine cut sequence, any bound on the separability ratio directly translates into a clean and simple dynamic programming for computing a maximum independent set of geometric objects. This paper focuses on the case when the objects are squares. For squares of arbitrary sizes, an Ω(1)-fraction can be separated (Abed et al., APPROX 2015), recently improved to 1/40 (and 1/160 ≈ 0.62% for the weighted case) (Khan and Pittu, APPROX 2020). We further improve this bound, showing that a 9/256 ≈ 3.51% can be separated for the weighted case. This result significantly narrows the possible range for squares to [3.51%, 50%]. The key to our improvement is a refined analysis of the existing framework.
Cite as

Parinya Chalermsook, Axel Kugelmann, Ly Orgo, Sumedha Uniyal, and Minoo Zarsav. An Improved Guillotine Cut for Squares. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 16:1-16:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{chalermsook_et_al:LIPIcs.WADS.2025.16,
  author =	{Chalermsook, Parinya and Kugelmann, Axel and Orgo, Ly and Uniyal, Sumedha and Zarsav, Minoo},
  title =	{{An Improved Guillotine Cut for Squares}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{16:1--16:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.16},
  URN =		{urn:nbn:de:0030-drops-242472},
  doi =		{10.4230/LIPIcs.WADS.2025.16},
  annote =	{Keywords: Guillotine cuts, Geometric Approximation Algorithms, Rectangles, Squares}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.17
Dynamic Streaming Algorithms for Geometric Independent Set

Authors: Timothy M. Chan and Yuancheng Yu

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
We present the first space-efficient, fully dynamic streaming algorithm for computing a constant-factor approximation of the maximum independent set size of n axis-aligned rectangles in two dimensions. For an arbitrarily small constant δ > 0, our algorithm obtains an O((1/δ)²) approximation and requires O(U^δ polylog n) space and update time with high probability, assuming that coordinates are integers bounded by U. We also obtain a similar result for fat objects in any constant dimension. This extends recent non-streaming algorithms by Bhore and Chan from SODA'25, and also greatly extends previous streaming results, which were limited to special types of geometric objects such as one-dimensional intervals and unit disks.
Cite as

Timothy M. Chan and Yuancheng Yu. Dynamic Streaming Algorithms for Geometric Independent Set. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 17:1-17:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{chan_et_al:LIPIcs.WADS.2025.17,
  author =	{Chan, Timothy M. and Yu, Yuancheng},
  title =	{{Dynamic Streaming Algorithms for Geometric Independent Set}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{17:1--17:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.17},
  URN =		{urn:nbn:de:0030-drops-242481},
  doi =		{10.4230/LIPIcs.WADS.2025.17},
  annote =	{Keywords: Geometric Independent Set, Dynamic Streaming Algorithms}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.53
Cut-Preserving Vertex Sparsifiers for Planar and Quasi-Bipartite Graphs

Authors: Yu Chen and Zihan Tan

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

Abstract
We study vertex sparsification for preserving cuts. Given a graph G with a subset |T| = k of its vertices called terminals, a quality-q cut sparsifier is a graph G' that contains T, such that, for any partition (T₁,T₂) of T into non-empty subsets, the value of the min-cut in G' separating T₁ from T₂ is within factor q from the value of the min-cut in G separating T₁ from T₂. The construction of cut sparsifiers with good (small) quality and size has been a central problem in graph compression for years. Planar graphs and quasi-bipartite graphs are two important special families studied in this research direction. The main results in this paper are new cut sparsifier constructions for them in the high-quality regime (where q = 1 or 1+{ε} for small {ε} > 0). We first show that every planar graph admits a planar quality-(1+{ε}) cut sparsifier of size Õ(k/poly({ε})), which is in sharp contrast with the lower bound of 2^{Ω(k)} for the quality-1 case. We then show that every quasi-bipartite graph admits a quality-1 cut sparsifier of size 2^{Õ(k²)}. This is the second to improve over the doubly-exponential bound for general graphs (previously only planar graphs have been shown to have single-exponential size quality-1 cut sparsifiers). Lastly, we show that contraction, a common approach for constructing cut sparsifiers adopted in most previous works, does not always give optimal bounds for cut sparsifiers. We demonstrate this by showing that the optimal size bound for quality-(1+{ε}) contraction-based cut sparsifiers for quasi-bipartite graphs lies in the range [k^{̃Ω(1/{ε})},k^{O(1/{ε}²)}], while in previous work an upper bound of Õ(k/{ε}²) was achieved via a non-contraction approach.
Cite as

Yu Chen and Zihan Tan. Cut-Preserving Vertex Sparsifiers for Planar and Quasi-Bipartite Graphs. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 53:1-53:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{chen_et_al:LIPIcs.ICALP.2025.53,
  author =	{Chen, Yu and Tan, Zihan},
  title =	{{Cut-Preserving Vertex Sparsifiers for Planar and Quasi-Bipartite Graphs}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{53:1--53:20},
  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.2025.53},
  URN =		{urn:nbn:de:0030-drops-234304},
  doi =		{10.4230/LIPIcs.ICALP.2025.53},
  annote =	{Keywords: Termianl Cut, Graph Sparsification}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.50
New Results on a General Class of Minimum Norm Optimization Problems

Authors: Kuowen Chen, Jian Li, Yuval Rabani, and Yiran Zhang

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

Abstract
We study the general norm optimization for combinatorial problems, initiated by Chakrabarty and Swamy (STOC 2019). We propose a general formulation that captures a large class of combinatorial structures: we are given a set 𝒰 of n weighted elements and a family of feasible subsets ℱ. Each subset S ∈ ℱ is called a feasible solution/set of the problem. We denote the value vector by v = {v_i}_{i ∈ [n]}, where v_i ≥ 0 is the value of element i. For any subset S ⊆ 𝒰, we use v[S] to denote the n-dimensional vector {v_e⋅ 𝟏[e ∈ S]}_{e ∈ 𝒰} (i.e., we zero out all entries that are not in S). Let f: ℝⁿ → ℝ_+ be a symmetric monotone norm function. Our goal is to minimize the norm objective f(v[S]) over feasible subset S ∈ ℱ. The problem significantly generalizes the corresponding min-sum and min-max problems. We present a general equivalent reduction of the norm minimization problem to a multi-criteria optimization problem with logarithmic budget constraints, up to a constant approximation factor. Leveraging this reduction, we obtain constant factor approximation algorithms for the norm minimization versions of several covering problems, such as interval cover, multi-dimensional knapsack cover, and logarithmic factor approximation for set cover. We also study the norm minimization versions for perfect matching, s-t path and s-t cut. We show the natural linear programming relaxations for these problems have a large integrality gap. To complement the negative result, we show that, for perfect matching, it is possible to obtain a bi-criteria result: for any constant ε,δ > 0, we can find in polynomial time a nearly perfect matching (i.e., a matching that matches at least 1-ε proportion of vertices) and its cost is at most (8+δ) times of the optimum for perfect matching. Moreover, we establish the existence of a polynomial-time O(log log n)-approximation algorithm for the norm minimization variant of the s-t path problem. Specifically, our algorithm achieves an α-approximation with a time complexity of n^{O(log log n / α)}, where 9 ≤ α ≤ log log n.
Cite as

Kuowen Chen, Jian Li, Yuval Rabani, and Yiran Zhang. New Results on a General Class of Minimum Norm Optimization Problems. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 50:1-50:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{chen_et_al:LIPIcs.ICALP.2025.50,
  author =	{Chen, Kuowen and Li, Jian and Rabani, Yuval and Zhang, Yiran},
  title =	{{New Results on a General Class of Minimum Norm Optimization Problems}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{50:1--50:20},
  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.2025.50},
  URN =		{urn:nbn:de:0030-drops-234276},
  doi =		{10.4230/LIPIcs.ICALP.2025.50},
  annote =	{Keywords: Approximation Algorithms, Minimum Norm Optimization, Linear Programming}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.132
Near-Optimal Algorithm for Directed Expander Decompositions

Authors: Aurelio L. Sulser and Maximilian Probst Gutenberg

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

Abstract
In this work, we present the first algorithm to compute expander decompositions in an m-edge directed graph with near-optimal time Õ(m). Further, our algorithm can maintain such a decomposition in a dynamic graph and again obtains near-optimal update times. Our result improves over previous algorithms [Bernstein et al., 2020; Hua et al., 2023] that only obtained algorithms optimal up to subpolynomial factors. In order to obtain our new algorithm, we present a new push-pull-relabel flow framework that generalizes the classic push-relabel flow algorithm [Goldberg and Tarjan, 1988] which was later dynamized for computing expander decompositions in undirected graphs [Henzinger et al., 2020; Saranurak and Wang, 2019]. We then show that the flow problems formulated in recent work [Hua et al., 2023] to decompose directed graphs can be solved much more efficiently in the push-pull-relabel flow framework. Recently, our algorithm has already been employed to obtain the currently fastest algorithm to compute min-cost flows [Van Den Brand et al., 2024]. We further believe that our algorithm can be used to speed-up and simplify recent breakthroughs in combinatorial graph algorithms towards fast maximum flow algorithms [Chuzhoy and Khanna, 2024; Chuzhoy and Khanna, 2024; Bernstein et al., 2024].
Cite as

Aurelio L. Sulser and Maximilian Probst Gutenberg. Near-Optimal Algorithm for Directed Expander Decompositions. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 132:1-132:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{sulser_et_al:LIPIcs.ICALP.2025.132,
  author =	{Sulser, Aurelio L. and Gutenberg, Maximilian Probst},
  title =	{{Near-Optimal Algorithm for Directed Expander Decompositions}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{132:1--132:20},
  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.2025.132},
  URN =		{urn:nbn:de:0030-drops-235096},
  doi =		{10.4230/LIPIcs.ICALP.2025.132},
  annote =	{Keywords: Directed Expander Decomposition, Push-Pull-Relabel Algorithm}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.33
Faster Construction of a Planar Distance Oracle with Õ(1) Query Time

Authors: Itai Boneh, Shay Golan, Shay Mozes, Daniel Prigan, and Oren Weimann

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

Abstract
We show how to preprocess a weighted undirected n-vertex planar graph in Õ(n^{4/3}) time, such that the distance between any pair of vertices can then be reported in Õ(1) time. This improves the previous Õ(n^{3/2}) preprocessing time [JACM'23]. Our main technical contribution is a near optimal construction of additively weighted Voronoi diagrams in undirected planar graphs. Namely, given a planar graph G and a face f, we show that one can preprocess G in Õ(n) time such that given any weight assignment to the vertices of f one can construct the additively weighted Voronoi diagram of f in near optimal Õ(|f|) time. This improves the Õ(√{n|f|}) construction time of [JACM'23].
Cite as

Itai Boneh, Shay Golan, Shay Mozes, Daniel Prigan, and Oren Weimann. Faster Construction of a Planar Distance Oracle with Õ(1) Query Time. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 33:1-33:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{boneh_et_al:LIPIcs.ICALP.2025.33,
  author =	{Boneh, Itai and Golan, Shay and Mozes, Shay and Prigan, Daniel and Weimann, Oren},
  title =	{{Faster Construction of a Planar Distance Oracle with \~{O}(1) Query Time}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{33:1--33:21},
  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.2025.33},
  URN =		{urn:nbn:de:0030-drops-234106},
  doi =		{10.4230/LIPIcs.ICALP.2025.33},
  annote =	{Keywords: Distance Oracle, Planar Graph, Construction Time}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.12
All-Subsets Important Separators with Applications to Sample Sets, Balanced Separators and Vertex Sparsifiers in Directed Graphs

Authors: Aditya Anand, Euiwoong Lee, Jason Li, and Thatchaphol Saranurak

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

Abstract
Given a directed graph G with n vertices and m edges, a parameter k and two disjoint subsets S,T ⊆ V(G), we show that the number of all-subsets important separators, which is the number of A-B important vertex separators of size at most k over all A ⊆ S and B ⊆ T, is at most β(|S|, |T|, k) = 4^k binom(|S|, ≤ k) binom(|T|, ≤ 2k), where binom(x, ≤ c) = ∑_{i = 1}^c binom(x,i), and that they can be enumerated in time 𝒪(β(|S|,|T|,k)k²(m+n)). This is a generalization of the folklore result stating that the number of A-B important separators for two fixed sets A and B is at most 4^k (first implicitly shown by Chen, Liu and Lu Algorithmica '09). From this result, we obtain the following applications: 1) We give a construction for detection sets and sample sets in directed graphs, generalizing the results of Kleinberg (Internet Mathematics' 03) and Feige and Mahdian (STOC' 06) to directed graphs. 2) Via our new sample sets, we give the first FPT algorithm for finding balanced separators in directed graphs parameterized by k, the size of the separator. Our algorithm runs in time 2^{𝒪(k)} ⋅ (m + n). 3) Additionally, we show a 𝒪(√{log k}) approximation algorithm for finding balanced separators in directed graphs in polynomial time. This improves the best known approximation guarantee of 𝒪(√{log n}) and matches the known guarantee in undirected graphs by Feige, Hajiaghayi and Lee (SICOMP' 08). 4) Finally, using our algorithm for listing all-subsets important separators, we give a deterministic construction of vertex cut sparsifiers in directed graphs when we are interested in preserving min-cuts of size upto c between bipartitions of the terminal set. Our algorithm constructs a sparsifier of size 𝒪(binom(t, ≤ 3c)2^{𝒪(c)}) and runs in time 𝒪(binom(t, ≤ 3c) 2^{𝒪(c)}(m + n)), where t is the number of terminals, and the sparsifier additionally preserves the set of important separators of size at most c between bipartitions of the terminals.
Cite as

Aditya Anand, Euiwoong Lee, Jason Li, and Thatchaphol Saranurak. All-Subsets Important Separators with Applications to Sample Sets, Balanced Separators and Vertex Sparsifiers in Directed Graphs. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 12:1-12:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{anand_et_al:LIPIcs.ICALP.2025.12,
  author =	{Anand, Aditya and Lee, Euiwoong and Li, Jason and Saranurak, Thatchaphol},
  title =	{{All-Subsets Important Separators with Applications to Sample Sets, Balanced Separators and Vertex Sparsifiers in Directed Graphs}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{12:1--12:20},
  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.2025.12},
  URN =		{urn:nbn:de:0030-drops-233892},
  doi =		{10.4230/LIPIcs.ICALP.2025.12},
  annote =	{Keywords: directed graphs, important separators, sample sets, balanced separators}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.39
Sampling with a Black Box: Faster Parameterized Approximation Algorithms for Vertex Deletion Problems

Authors: Barış Can Esmer and Ariel Kulik

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

Abstract
In this paper, we present Sampling with a Black Box, a unified framework for the design of parameterized approximation algorithms for vertex deletion problems (e.g., Vertex Cover, Feedback Vertex Set, etc.). The framework relies on two components: - A Sampling Step. A polynomial-time randomized algorithm that, given a graph G, returns a random vertex v such that the optimum of G⧵ {v} is smaller by 1 than the optimum of G, with some prescribed probability q. We show that such algorithms exist for multiple vertex deletion problems. - A Black Box algorithm which is either an exact parameterized algorithm, a polynomial-time approximation algorithm, or a parameterized-approximation algorithm. The framework combines these two components together. The sampling step is applied iteratively to remove vertices from the input graph, and then the solution is extended using the black box algorithm. The process is repeated sufficiently many times so that the target approximation ratio is attained with a constant probability. We use the technique to derive parameterized approximation algorithms for several vertex deletion problems, including Feedback Vertex Set, d-Hitting Set and 𝓁-Path Vertex Cover. In particular, for every approximation ratio 1 < β < 2, we attain a parameterized β-approximation for Feedback Vertex Set, which is faster than the parameterized β-approximation of [Jana, Lokshtanov, Mandal, Rai and Saurabh, MFCS 23']. Furthermore, our algorithms are always faster than the algorithms attained using Fidelity Preserving Transformations [Fellows, Kulik, Rosamond, and Shachnai, JCSS 18'].
Cite as

Barış Can Esmer and Ariel Kulik. Sampling with a Black Box: Faster Parameterized Approximation Algorithms for Vertex Deletion Problems. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 39:1-39:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{canesmer_et_al:LIPIcs.ICALP.2025.39,
  author =	{Can Esmer, Bar{\i}\c{s} and Kulik, Ariel},
  title =	{{Sampling with a Black Box: Faster Parameterized Approximation Algorithms for Vertex Deletion Problems}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{39:1--39:20},
  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.2025.39},
  URN =		{urn:nbn:de:0030-drops-234165},
  doi =		{10.4230/LIPIcs.ICALP.2025.39},
  annote =	{Keywords: Parameterized Approximation Algorithms, Random Sampling}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.69
Approximation Algorithms for Optimal Hopsets

Authors: Michael Dinitz, Ama Koranteng, and Yasamin Nazari

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

Abstract
For a given graph G, a hopset H with hopbound β and stretch α is a set of edges such that between every pair of vertices u and v, there is a path with at most β hops in G ∪ H that approximates the distance between u and v up to a multiplicative stretch of α. Hopsets have found a wide range of applications for distance-based problems in various computational models since the 90s. More recently, there has been significant interest in understanding these fundamental objects from an existential and structural perspective. But all of this work takes a worst-case (or existential) point of view: How many edges do we need to add to satisfy a given hopbound and stretch requirement for any input graph? We initiate the study of the natural optimization variant of this problem: given a specific graph instance, what is the minimum number of edges that satisfy the hopbound and stretch requirements? We give approximation algorithms for a generalized hopset problem which, when combined with known existential bounds, lead to different approximation guarantees for various regimes depending on hopbound, stretch, and directed vs. undirected inputs. We complement our upper bounds with a lower bound that implies Label Cover hardness for directed hopsets and shortcut sets with hopbound at least 3.
Cite as

Michael Dinitz, Ama Koranteng, and Yasamin Nazari. Approximation Algorithms for Optimal Hopsets. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 69:1-69:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{dinitz_et_al:LIPIcs.ICALP.2025.69,
  author =	{Dinitz, Michael and Koranteng, Ama and Nazari, Yasamin},
  title =	{{Approximation Algorithms for Optimal Hopsets}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{69:1--69:20},
  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.2025.69},
  URN =		{urn:nbn:de:0030-drops-234464},
  doi =		{10.4230/LIPIcs.ICALP.2025.69},
  annote =	{Keywords: Hopsets, Approximation Algorithms}
}
  • Refine by Type
  • 35 Document/PDF
  • 19 Document/HTML

  • Refine by Publication Year
  • 20 2025
  • 3 2024
  • 2 2023
  • 1 2022
  • 2 2020
  • Show More...

  • Refine by Author
  • 15 Chalermsook, Parinya
  • 4 Saranurak, Thatchaphol
  • 3 Bentert, Matthias
  • 3 Fomin, Fedor V.
  • 3 Orgo, Ly
  • Show More...

  • Refine by Series/Journal
  • 34 LIPIcs
  • 1 DagRep

  • Refine by Classification
  • 7 Theory of computation → Approximation algorithms analysis
  • 4 Theory of computation → Data structures design and analysis
  • 4 Theory of computation → Fixed parameter tractability
  • 4 Theory of computation → Graph algorithms analysis
  • 3 Theory of computation → Computational geometry
  • Show More...

  • Refine by Keyword
  • 8 Approximation Algorithms
  • 4 approximation algorithms
  • 3 Clustering
  • 3 Rectangles
  • 2 Binary Search Tree
  • Show More...

Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact