18 Search Results for "Lingas, Andrzej"

Document
DOI: 10.4230/LIPIcs.ITCS.2026.3
Linear Matroid Intersection Is in Catalytic Logspace

Authors: Aryan Agarwala, Yaroslav Alekseev, and Antoine Vinciguerra

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
Linear matroid intersection is an important problem in combinatorial optimization. Given two linear matroids over the same ground set, the linear matroid intersection problem asks you to find a common independent set of maximum size. The deep interest in linear matroid intersection is due to the fact that it generalises many classical problems in theoretical computer science, such as bipartite matching, edge disjoint spanning trees, rainbow spanning tree, and many more. We study this problem in the model of catalytic computation: space-bounded machines are granted access to catalytic space, which is additional working memory that is full with arbitrary data that must be preserved at the end of its computation. Although linear matroid intersection has had a polynomial time algorithm for over 50 years, it remains an important open problem to show that linear matroid intersection belongs to any well studied subclass of {P}. We address this problem for the class catalytic logspace (CL) with a polynomial time bound (CLP). Recently, Agarwala and Mertz (2025) showed that bipartite maximum matching can be computed in the class CLP ⊆ {P}. This was the first subclass of {P} shown to contain bipartite matching, and additionally the first problem outside TC¹ shown to be contained in CL. We significantly improve the result of Agarwala and Mertz by showing that linear matroid intersection can be computed in CLP.
Cite as

Aryan Agarwala, Yaroslav Alekseev, and Antoine Vinciguerra. Linear Matroid Intersection Is in Catalytic Logspace. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 3:1-3:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{agarwala_et_al:LIPIcs.ITCS.2026.3,
  author =	{Agarwala, Aryan and Alekseev, Yaroslav and Vinciguerra, Antoine},
  title =	{{Linear Matroid Intersection Is in Catalytic Logspace}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{3:1--3:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.3},
  URN =		{urn:nbn:de:0030-drops-252908},
  doi =		{10.4230/LIPIcs.ITCS.2026.3},
  annote =	{Keywords: Catalytic Computing, Computational Complexity, Matroid Theory, Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.31
Delaunay Triangulations with Predictions

Authors: Sergio Cabello, Timothy M. Chan, and Panos Giannopoulos

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
We investigate algorithms with predictions in computational geometry, specifically focusing on the basic problem of computing 2D Delaunay triangulations. Given a set P of n points in the plane and a triangulation G that serves as a "prediction" of the Delaunay triangulation, we would like to use G to compute the correct Delaunay triangulation DT(P) more quickly when G is "close" to DT(P). We obtain a variety of results of this type, under different deterministic and probabilistic settings, including the following: 1) Define D to be the number of edges in G that are not in DT(P). We present a deterministic algorithm to compute DT(P) from G in O(n + Dlog³ n) time, and a randomized algorithm in O(n+Dlog n) expected time, the latter of which is optimal in terms of D. 2) Let R be a random subset of the edges of DT(P), where each edge is chosen independently with probability ρ. Suppose G is any triangulation of P that contains R. We present an algorithm to compute DT(P) from G in O(nlog log n + nlog(1/ρ)) time with high probability. 3) Define d_{vio} to be the maximum number of points of P strictly inside the circumcircle of a triangle in G (the number is 0 if G is equal to DT(P)). We present a deterministic algorithm to compute DT(P) from G in O(nlog^*n + nlog d_{vio}) time. We also obtain results in similar settings for related problems such as 2D Euclidean minimum spanning trees, and hope that our work will open up a fruitful line of future research.
Cite as

Sergio Cabello, Timothy M. Chan, and Panos Giannopoulos. Delaunay Triangulations with Predictions. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 31:1-31:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{cabello_et_al:LIPIcs.ITCS.2026.31,
  author =	{Cabello, Sergio and Chan, Timothy M. and Giannopoulos, Panos},
  title =	{{Delaunay Triangulations with Predictions}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{31:1--31:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.31},
  URN =		{urn:nbn:de:0030-drops-253186},
  doi =		{10.4230/LIPIcs.ITCS.2026.31},
  annote =	{Keywords: Delaunay Triangulation, Minimum Spanning Tree, Algorithms with Predictions}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2025.14
Optimal-Length Labeling Schemes for Fast Deterministic Communication in Radio Networks

Authors: Adam Ganczorz, Tomasz Jurdzinski, and Andrzej Pelc

Published in: LIPIcs, Volume 361, 29th International Conference on Principles of Distributed Systems (OPODIS 2025)

Abstract
We consider two fundamental communication tasks in arbitrary radio networks: broadcasting (information from one source has to reach all nodes) and gossiping (every node has a message and all messages have to reach all nodes). Nodes are assigned labels that are (not necessarily different) binary strings. Each node knows its own label and can use it as a parameter in the same deterministic algorithm. The length of a labeling scheme is the largest length of a label. The goal is to find labeling schemes of asymptotically optimal length for the above tasks, and to design fast deterministic distributed algorithms for each of them, using labels of optimal length. Our main result concerns broadcasting. We show the existence of a labeling scheme of constant length that supports broadcasting in time O(D+log² n), where D is the diameter of the network and n is the number of nodes. This broadcasting time is an improvement over the best currently known O(Dlog n + log² n) time of broadcasting with constant-length labels, due to Ellen and Gilbert (SPAA 2020). It also matches the optimal broadcasting time in radio networks of known topology. Hence, we show that appropriately chosen node labels of constant length permit to achieve, in a distributed way, the optimal centralized broadcasting time. This is, perhaps, the most surprising finding of this paper. We are able to obtain our result thanks to a novel methodological tool of propagating information in radio networks, that we call a 2-height respecting tree. Next, we apply our broadcasting algorithm to solve the gossiping problem. We get a gossiping algorithm working in time O(D + Δlog n + log² n), using a labeling scheme of optimal length O(log Δ), where Δ is the maximum degree. Our time is the same as the best known gossiping time in radio networks of known topology.
Cite as

Adam Ganczorz, Tomasz Jurdzinski, and Andrzej Pelc. Optimal-Length Labeling Schemes for Fast Deterministic Communication in Radio Networks. In 29th International Conference on Principles of Distributed Systems (OPODIS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 361, pp. 14:1-14:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ganczorz_et_al:LIPIcs.OPODIS.2025.14,
  author =	{Ganczorz, Adam and Jurdzinski, Tomasz and Pelc, Andrzej},
  title =	{{Optimal-Length Labeling Schemes for Fast Deterministic Communication in Radio Networks}},
  booktitle =	{29th International Conference on Principles of Distributed Systems (OPODIS 2025)},
  pages =	{14:1--14:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-409-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{361},
  editor =	{Arusoaie, Andrei and Onica, Emanuel and Spear, Michael and Tucci-Piergiovanni, Sara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2025.14},
  URN =		{urn:nbn:de:0030-drops-251874},
  doi =		{10.4230/LIPIcs.OPODIS.2025.14},
  annote =	{Keywords: radio network, distributed algorithms, algorithms with advice, labeling scheme, broadcasting, gossiping}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.8
Binary k-Center with Missing Entries: Structure Leads to Tractability

Authors: Tobias Friedrich, Kirill Simonov, and Farehe Soheil

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
k-Center clustering is a fundamental classification problem, where the task is to categorize the given collection of entities into k clusters and come up with a representative for each cluster, so that the maximum distance between an entity and its representative is minimized. In this work, we focus on the setting where the entities are represented by binary vectors with missing entries, which model incomplete categorical data. This version of the problem has wide applications, from predictive analytics to bioinformatics. Our main finding is that the problem, which is notoriously hard from the classical complexity viewpoint, becomes tractable as soon as the known entries are sparse and exhibit a certain structure. Formally, we show fixed-parameter tractable algorithms for the parameters vertex cover, fracture number, and treewidth of the row-column graph, which encodes the positions of the known entries of the matrix. Additionally, we tie the complexity of the 1-cluster variant of the problem, which is famous under the name Closest String, to the complexity of solving integer linear programs with few constraints. This implies, in particular, that improving upon the running times of our algorithms would lead to more efficient algorithms for integer linear programming in general.
Cite as

Tobias Friedrich, Kirill Simonov, and Farehe Soheil. Binary k-Center with Missing Entries: Structure Leads to Tractability. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 8:1-8:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{friedrich_et_al:LIPIcs.IPEC.2025.8,
  author =	{Friedrich, Tobias and Simonov, Kirill and Soheil, Farehe},
  title =	{{Binary k-Center with Missing Entries: Structure Leads to Tractability}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{8:1--8:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.8},
  URN =		{urn:nbn:de:0030-drops-251403},
  doi =		{10.4230/LIPIcs.IPEC.2025.8},
  annote =	{Keywords: Clustering, Missing Entries, k-Center, Parameterized Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.47
Hardness and Fixed Parameter Tractability for Pinwheel Scheduling Problems

Authors: Yusuke Kobayashi and Bingkai Lin

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
In the Pinwheel Packing problem, we are given a set of recurring tasks, each associated with a positive integer a_i for task i. The objective is to select one task to perform each day such that every task i is performed at least once within every a_i consecutive days. The exact computational complexity of this problem, where ∑ 1/a_i = 1, has remained an open question for more than 30 years; in particular, it is still unknown whether the problem is NP-hard. The first contribution of this paper is to show that Pinwheel Packing cannot be solved in polynomial time under a standard complexity assumption, improving upon the hardness result shown by Jacobs and Longo. Additionally, we present fixed-parameter algorithms for variants of Pinwheel Packing, parameterized by the number of tasks.
Cite as

Yusuke Kobayashi and Bingkai Lin. Hardness and Fixed Parameter Tractability for Pinwheel Scheduling Problems. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 47:1-47:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kobayashi_et_al:LIPIcs.ISAAC.2025.47,
  author =	{Kobayashi, Yusuke and Lin, Bingkai},
  title =	{{Hardness and Fixed Parameter Tractability for Pinwheel Scheduling Problems}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{47:1--47:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.47},
  URN =		{urn:nbn:de:0030-drops-249558},
  doi =		{10.4230/LIPIcs.ISAAC.2025.47},
  annote =	{Keywords: Pinwheel Scheduling, Polynomial-time Solvability, Packing and Covering, Fixed Parameter Algorithms}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2025.58
Brief Announcement: Optimal-Length Labeling Schemes for Fast Deterministic Communication in Radio Networks

Authors: Adam Ganczorz, Tomasz Jurdzinski, and Andrzej Pelc

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

Abstract
We consider two fundamental communication tasks in arbitrary radio networks: broadcasting (information from one source has to reach all nodes) and gossiping (every node has a message and all messages have to reach all nodes). Nodes are assigned labels that are (not necessarily different) binary strings. Each node knows its own label and can use it as a parameter in the same deterministic algorithm. The length of a labeling scheme is the largest length of a label. The goal is to find labeling schemes of asymptotically optimal length for the above tasks, and to design fast deterministic distributed algorithms for each of them, using labels of optimal length. Our main result concerns broadcasting. We show the existence of a labeling scheme of constant length that supports broadcasting in time O(D+log² n), where D is the diameter of the network and n is the number of nodes. This broadcasting time is an improvement over the best currently known O(Dlog n + log² n) time of broadcasting with constant-length labels, due to Ellen and Gilbert (SPAA 2020). It also matches the optimal broadcasting time in radio networks of known topology. Hence, we show that appropriately chosen node labels of constant length permit to achieve, in a distributed way, the optimal centralized broadcasting time. This is, perhaps, the most surprising finding of this paper. We are able to obtain our result thanks to a novel methodological tool of propagating information in radio networks, that we call a 2-height respecting tree. Next, we apply our broadcasting algorithm to solve the gossiping problem. We get a gossiping algorithm working in time O(D + Δlog n + log² n), using a labeling scheme of optimal length O(log Δ), where Δ is the maximum degree. Our time is the same as the best known gossiping time in radio networks of known topology.
Cite as

Adam Ganczorz, Tomasz Jurdzinski, and Andrzej Pelc. Brief Announcement: Optimal-Length Labeling Schemes for Fast Deterministic Communication in Radio Networks. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 58:1-58:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ganczorz_et_al:LIPIcs.DISC.2025.58,
  author =	{Ganczorz, Adam and Jurdzinski, Tomasz and Pelc, Andrzej},
  title =	{{Brief Announcement: Optimal-Length Labeling Schemes for Fast Deterministic Communication in Radio Networks}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{58:1--58:8},
  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.2025.58},
  URN =		{urn:nbn:de:0030-drops-248744},
  doi =		{10.4230/LIPIcs.DISC.2025.58},
  annote =	{Keywords: radio network, distributed algorithms, algorithms with advice, labeling scheme, broadcasting, gossiping}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.54
Non-Boolean OMv: One More Reason to Believe Lower Bounds for Dynamic Problems

Authors: Bingbing Hu and Adam Polak

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

Abstract
Most of the known tight lower bounds for dynamic problems are based on the Online Boolean Matrix-Vector Multiplication (OMv) Hypothesis, which is not as well studied and understood as some more popular hypotheses in fine-grained complexity. It would be desirable to base hardness of dynamic problems on a more believable hypothesis. We propose analogues of the OMv Hypothesis for variants of matrix multiplication that are known to be harder than Boolean product in the offline setting, namely: equality, dominance, min-witness, min-max, and bounded monotone min-plus products. These hypotheses are a priori weaker assumptions than the standard (Boolean) OMv Hypothesis and yet we show that they are actually equivalent to it. This establishes the first such fine-grained equivalence class for dynamic problems.
Cite as

Bingbing Hu and Adam Polak. Non-Boolean OMv: One More Reason to Believe Lower Bounds for Dynamic Problems. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 54:1-54:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hu_et_al:LIPIcs.ESA.2025.54,
  author =	{Hu, Bingbing and Polak, Adam},
  title =	{{Non-Boolean OMv: One More Reason to Believe Lower Bounds for Dynamic Problems}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{54:1--54:16},
  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.2025.54},
  URN =		{urn:nbn:de:0030-drops-245228},
  doi =		{10.4230/LIPIcs.ESA.2025.54},
  annote =	{Keywords: Fine-grained complexity, OMv hypothesis, reductions, equivalence class}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.5
External-Memory Priority Queues with Optimal Insertions

Authors: Gerth Stølting Brodal, Michael T. Goodrich, John Iacono, Jared Lo, Ulrich Meyer, Victor Pagan, Nodari Sitchinava, and Rolf Svenning

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

Abstract
We present an external-memory priority queue structure supporting Insert and DeleteMin with amortized 𝒪(1) and 𝒪(lg N) comparisons, respectively, and amortized 𝒪(1/B) and 𝒪(1/B log_{M/B} N/B) I/Os, respectively. Here, M is the size of the internal memory, B is the block size of I/Os between internal and external memory, and N is the number of elements in the priority queue just before an operation is performed. Previous external-memory priority queues required amortized 𝒪(lg N) comparisons and 𝒪(1/B log_{M/B} N/B) I/Os for both Insert and DeleteMin. The construction requires the minimal assumption M ≥ 2B.
Cite as

Gerth Stølting Brodal, Michael T. Goodrich, John Iacono, Jared Lo, Ulrich Meyer, Victor Pagan, Nodari Sitchinava, and Rolf Svenning. External-Memory Priority Queues with Optimal Insertions. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 5:1-5:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{brodal_et_al:LIPIcs.ESA.2025.5,
  author =	{Brodal, Gerth St{\o}lting and Goodrich, Michael T. and Iacono, John and Lo, Jared and Meyer, Ulrich and Pagan, Victor and Sitchinava, Nodari and Svenning, Rolf},
  title =	{{External-Memory Priority Queues with Optimal Insertions}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{5:1--5:14},
  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.2025.5},
  URN =		{urn:nbn:de:0030-drops-244734},
  doi =		{10.4230/LIPIcs.ESA.2025.5},
  annote =	{Keywords: priority queues, external memory, cache aware, amortized complexity}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.27
Triangles Improve 0.878 Approximation for Maxcut

Authors: Fredie George, Anand Louis, and Rameesh Paul

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

Abstract
Maxcut is a fundamental problem in graph algorithms, extensively studied for its theoretical and practical significance. The goal is to partition the vertex set of a graph G = (V, E) into disjoint subsets S and V⧵S so as to maximize the number of edges crossing the cut (S,V⧵S). The seminal work of Goemans and Williamson [Goemans and Williamson, 1995] introduced a semidefinite programming (SDP) based algorithm achieving a α_{GW} ≈ 0.87856-approximation for general graphs, guaranteed to be optimal under the Unique Games Conjecture [Khot, 2002; Khot et al., 2007]. We revisit the Goemans–Williamson SDP and prove that the standard Maxcut SDP achieves a (α_{GW} + Ω(1))-approximation whenever the input graph contains Ω(|E|) edge-disjoint triangles. Our analysis builds on classical rounding techniques studied in [Goemans and Williamson, 1995; Zwick, 1999] and introduces a refined understanding of the SDP solution structure in regimes where the previous guarantees are tight. Our result identifies a simple combinatorial property that may be satisfied by many natural graph classes. As applications, we show that unit ball graphs and graphs satisfying a spectral transitivity condition (as studied in [Gupta et al., 2016; Basu et al., 2024]) meet our structural criterion, and therefore we get better than α_{GW} approximation guarantees for them. Our algorithm runs in nearly linear time 𝒪̃(|E|), offering a more practical alternative to the PTAS of [Jansen et al., 2005] for unit ball graphs, which has exponential dependence on the approximation parameter.
Cite as

Fredie George, Anand Louis, and Rameesh Paul. Triangles Improve 0.878 Approximation for Maxcut. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 27:1-27:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{george_et_al:LIPIcs.APPROX/RANDOM.2025.27,
  author =	{George, Fredie and Louis, Anand and Paul, Rameesh},
  title =	{{Triangles Improve 0.878 Approximation for Maxcut}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{27:1--27:25},
  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.2025.27},
  URN =		{urn:nbn:de:0030-drops-243931},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.27},
  annote =	{Keywords: Approximation Algorithms, Maxcut, Semidefinite Programming, Edge-disjoint Triangles, Unit Ball Graphs, Spectral Triadic Graphs}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.15
A Polynomial-Time Approximation Algorithm for Complete Interval Minors

Authors: Romain Bourneuf, Julien Cocquet, Chaoliang Tang, and Stéphan Thomassé

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

Abstract
As shown by Robertson and Seymour, deciding whether the complete graph K_t is a minor of an input graph G is a fixed parameter tractable problem when parameterized by t. From the approximation viewpoint, a substantial gap remains: there is no PTAS for finding the largest complete minor unless P = NP, whereas the best known result is a polytime O(√ n)-approximation algorithm by Alon, Lingas and Wahlén. We investigate the complexity of finding K_t as interval minor in ordered graphs (i.e. graphs with a linear order on the vertices, in which intervals are contracted to form minors). Our main result is a polytime f(t)-approximation algorithm, where f is triply exponential in t but independent of n. The algorithm is based on delayed decompositions and shows that ordered graphs without a K_t interval minor can be constructed via a bounded number of three operations: closure under substitutions, edge union, and concatenation of a stable set. As a byproduct, graphs avoiding K_t as an interval minor have bounded chromatic number.
Cite as

Romain Bourneuf, Julien Cocquet, Chaoliang Tang, and Stéphan Thomassé. A Polynomial-Time Approximation Algorithm for Complete Interval Minors. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 15:1-15:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bourneuf_et_al:LIPIcs.APPROX/RANDOM.2025.15,
  author =	{Bourneuf, Romain and Cocquet, Julien and Tang, Chaoliang and Thomass\'{e}, St\'{e}phan},
  title =	{{A Polynomial-Time Approximation Algorithm for Complete Interval Minors}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{15:1--15:23},
  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.2025.15},
  URN =		{urn:nbn:de:0030-drops-243814},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.15},
  annote =	{Keywords: Approximation algorithm, Ordered graphs, Interval minors, Delayed decompositions}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.34
Link Diameter, Radius and 2-Point Link Distance Queries in Polygonal Domains

Authors: Mart Hagedoorn and Valentin Polishchuk

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

Abstract
We show how to preprocess a polygonal domain with holes so that the link distance (the number of links in a minimum-link path) between two query points in the domain can be reported efficiently. Using our data structures, the link diameter of the domain (i.e., the maximum number of links that may be required in a minimum-link path between two points in the domain) as well as the link center and radius of the domain (i.e., the point minimizing the maximum link distance to the furthest point in the domain and this maximum link distance) can be found in polynomial time. We also give a simpler algorithm for finding the link diameter, not using the link distance query structures. Answering 2-point link distance queries and computing the link diameter/radius/center in polygonal domains have been open questions since these problems were studied for simple polygons in the 90’s.
Cite as

Mart Hagedoorn and Valentin Polishchuk. Link Diameter, Radius and 2-Point Link Distance Queries in Polygonal Domains. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 34:1-34:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hagedoorn_et_al:LIPIcs.WADS.2025.34,
  author =	{Hagedoorn, Mart and Polishchuk, Valentin},
  title =	{{Link Diameter, Radius and 2-Point Link Distance Queries in Polygonal Domains}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{34:1--34:15},
  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.2025.34},
  URN =		{urn:nbn:de:0030-drops-242659},
  doi =		{10.4230/LIPIcs.WADS.2025.34},
  annote =	{Keywords: Minimum-link paths, link distance, diameter, center, radius, 2-point distance queries}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.43
On the Complexity of Finding 1-Center Spanning Trees

Authors: Pin-Hsian Lee, Meng-Tsung Tsai, and Hung-Lung Wang

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

Abstract
We consider the problem of finding a spanning tree T of a given undirected graph G such that any other spanning tree can be obtained from T by removing k edges and subsequently adding k edges, where k is minimized over all spanning trees of G. We refer to this minimum k as the treeradius of G. Treeradius is an interesting graph parameter with natural interpretations: (1) It is the smallest radius of a Hamming ball centered at an extreme point of the spanning tree polytope that covers the entire polytope. (2) Any graph with bounded treeradius also has bounded treewidth. Consequently, if a problem admits a fixed-parameter algorithm parameterized by treewidth, it also admits a fixed-parameter algorithm parameterized by treeradius. In this paper, we show that computing the exact treeradius for n-vertex graphs requires 2^Ω(n) time under the Exponential Time Hypothesis (ETH) and does not admit a PTAS, with an inapproximability bound of 1153/1152, unless P = NP. This hardness result is surprising, as treeradius has significantly higher ETH complexity compared to analogous problems on shortest path polytopes and star subgraph polytopes.
Cite as

Pin-Hsian Lee, Meng-Tsung Tsai, and Hung-Lung Wang. On the Complexity of Finding 1-Center Spanning Trees. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 43:1-43:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lee_et_al:LIPIcs.WADS.2025.43,
  author =	{Lee, Pin-Hsian and Tsai, Meng-Tsung and Wang, Hung-Lung},
  title =	{{On the Complexity of Finding 1-Center Spanning Trees}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{43:1--43:19},
  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.2025.43},
  URN =		{urn:nbn:de:0030-drops-242743},
  doi =		{10.4230/LIPIcs.WADS.2025.43},
  annote =	{Keywords: Treeradius, Spanning tree polytope, Shortest s, t-path polytope}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2025.152
Tree Algebras and Bisimulation-Invariant MSO on Finite Graphs

Authors: Thomas Colcombet, Amina Doumane, and Denis Kuperberg

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

Abstract
We establish that the bisimulation invariant fragment of MSO over finite transition systems is expressively equivalent over finite transition systems to modal μ-calculus, a question that had remained open for several decades. The proof goes by translating the question to an algebraic framework, and showing that the languages of regular trees that are recognised by finitary tree algebras whose sorts zero and one are finite are the regular ones. This corresponds for trees to a weak form of the key translation of Wilke algebras to omega-semigroup over infinite words, and was also a missing piece in the algebraic theory of regular languages of infinite trees for twenty years.
Cite as

Thomas Colcombet, Amina Doumane, and Denis Kuperberg. Tree Algebras and Bisimulation-Invariant MSO on Finite Graphs. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 152:1-152:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{colcombet_et_al:LIPIcs.ICALP.2025.152,
  author =	{Colcombet, Thomas and Doumane, Amina and Kuperberg, Denis},
  title =	{{Tree Algebras and Bisimulation-Invariant MSO on Finite Graphs}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{152:1--152:16},
  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.2025.152},
  URN =		{urn:nbn:de:0030-drops-235294},
  doi =		{10.4230/LIPIcs.ICALP.2025.152},
  annote =	{Keywords: MSO, mu-calculus, finite graphs, bisimulation, tree algebra}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.8
Rapid Mixing of the Flip Chain over Non-Crossing Spanning Trees

Authors: Konrad Anand, Weiming Feng, Graham Freifeld, Heng Guo, Mark Jerrum, and Jiaheng Wang

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

Abstract
We show that the flip chain for non-crossing spanning trees of n+1 points in convex position mixes in time O(n⁸log n). We use connections between Fuss-Catalan structures to construct a comparison argument with a chain similar to Wilson’s lattice path chain (Wilson 2004).
Cite as

Konrad Anand, Weiming Feng, Graham Freifeld, Heng Guo, Mark Jerrum, and Jiaheng Wang. Rapid Mixing of the Flip Chain over Non-Crossing Spanning Trees. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{anand_et_al:LIPIcs.SoCG.2025.8,
  author =	{Anand, Konrad and Feng, Weiming and Freifeld, Graham and Guo, Heng and Jerrum, Mark and Wang, Jiaheng},
  title =	{{Rapid Mixing of the Flip Chain over Non-Crossing Spanning Trees}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{8:1--8:18},
  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.2025.8},
  URN =		{urn:nbn:de:0030-drops-231607},
  doi =		{10.4230/LIPIcs.SoCG.2025.8},
  annote =	{Keywords: non-crossing spanning trees, Markov chain, mixing time}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.73
Dominating Set, Independent Set, Discrete k-Center, Dispersion, and Related Problems for Planar Points in Convex Position

Authors: Anastasiia Tkachenko and Haitao Wang

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

Abstract
Given a set P of n points in the plane, its unit-disk graph G(P) is a graph with P as its vertex set such that two points of P are connected by an edge if their (Euclidean) distance is at most 1. We consider several classical problems on G(P) in a special setting when points of P are in convex position. These problems are all NP-hard in the general case. We present efficient algorithms for these problems under the convex position assumption. ● For the problem of finding the smallest dominating set of G(P), we present an O(knlog n) time algorithm, where k is the smallest dominating set size. We also consider the weighted case in which each point of P has a weight and the goal is to find a dominating set in G(P) with minimum total weight; our algorithm runs in O(n³log² n) time. In particular, for a given k, our algorithm can compute in O(kn²log² n) time a minimum weight dominating set of size at most k (if it exists). ● For the discrete k-center problem, which is to find a subset of k points in P (called centers) for a given k, such that the maximum distance between any point in P and its nearest center is minimized. We present an algorithm that solves the problem in O(min{n^{4/3}log n+knlog² n,k² nlog²n}) time, which is O(n²log² n) in the worst case when k = Θ(n). For comparison, the runtime of the current best algorithm for the continuous version of the problem where centers can be anywhere in the plane is O(n³ log n). ● For the problem of finding a maximum independent set in G(P), we give an algorithm of O(n^{7/2}) time and another randomized algorithm of O(n^{37/11}) expected time, which improve the previous best result of O(n⁶log n) time. Our algorithms can be extended to compute a maximum-weight independent set in G(P) with the same time complexities when points of P have weights. - If we are looking for an (unweighted) independent set of size 3, we derive an algorithm of O(nlog n) time; the previous best algorithm runs in O(n^{4/3}log² n) time (which works for the general case where points of P are not necessarily in convex position). - If points of P have weights and are not necessarily in convex position, we present an algorithm that can find a maximum-weight independent set of size 3 in O(n^{5/3+δ}) time for an arbitrarily small constant δ > 0. By slightly modifying the algorithm, a maximum-weight clique of size 3 can also be found within the same time complexity. ● For the dispersion problem, which is to find a subset of k points from P for a given k, such that the minimum pairwise distance of the points in the subset is maximized. We present an algorithm of O(n^{7/2}log n) time and another randomized algorithm of O(n^{37/11}log n) expected time, which improve the previous best result of O(n⁶) time. - If k = 3, we present an algorithm of O(nlog² n) time and another randomized algorithm of O(nlog n) expected time; the previous best algorithm runs in O(n^{4/3}log² n) time (which works for the general case where points of P are not necessarily in convex position).
Cite as

Anastasiia Tkachenko and Haitao Wang. Dominating Set, Independent Set, Discrete k-Center, Dispersion, and Related Problems for Planar Points in Convex Position. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 73:1-73:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{tkachenko_et_al:LIPIcs.STACS.2025.73,
  author =	{Tkachenko, Anastasiia and Wang, Haitao},
  title =	{{Dominating Set, Independent Set, Discrete k-Center, Dispersion, and Related Problems for Planar Points in Convex Position}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{73:1--73:20},
  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.2025.73},
  URN =		{urn:nbn:de:0030-drops-228982},
  doi =		{10.4230/LIPIcs.STACS.2025.73},
  annote =	{Keywords: Dominating set, k-center, geometric set cover, independent set, clique, vertex cover, unit-disk graphs, convex position, dispersion, maximally separated sets}
}
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