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Volume

LIPIcs, Volume 317

Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

APPROX/RANDOM 2024, August 28-30, 2024, London School of Economics, London, UK

Editors: Amit Kumar and Noga Ron-Zewi

Volume

LIPIcs, Volume 13

IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)

FSTTCS 2011, December 12-14, 2011, Mumbai, India

Editors: Supratik Chakraborty and Amit Kumar

Document

DOI: 10.4230/LIPIcs.SEA.2026.3

Approximation Algorithms for Budget Splitting in Multi-Channel Influence Maximization

Authors: Dildar Ali, Ansh Jasrotia, Abishek Salaria, and Suman Banerjee

Published in: LIPIcs, Volume 371, 24th International Symposium on Experimental Algorithms (SEA 2026)

Abstract

How to utilize an allocated budget effectively for branding and promotion of a commercial house is an important problem, particularly when multiple advertising media are available. There exist multiple such media, and among them, two popular ones are billboards and social media advertisements. In this context, the question naturally arises: how should a budget be allocated to maximize total influence? Although there is significant literature on the effective use of budgets in individual advertising media, there are hardly any studies examining budget allocation across multiple advertising media. To bridge this gap, this paper introduces the Budget Splitting Problem in Billboard and Social Network Advertisement. We introduce the notion of interaction effect to capture the additional influence due to triggers from multiple media of advertising. Using this notion, we propose a noble influence function Φ(,) that captures the total influence and shows that this function is non-negative, monotone, and non-bisubmodular. We introduce bi-submodularity ratio (γ) and generalized curvature (α) to measure how close a function is to being bi-submodular and how far a function is from being modular, respectively. We propose the Randomized Greedy and Two-Phase Adaptive Greedy approach, where the influence function is non-bisubmodular and achieves an approximation guarantee of (1/α)(1-e^(-γα)). We conducted several experiments using real-world datasets and observed that the proposed solution approach’s budget splitting leads to a greater influence than existing approaches.

Cite as

Dildar Ali, Ansh Jasrotia, Abishek Salaria, and Suman Banerjee. Approximation Algorithms for Budget Splitting in Multi-Channel Influence Maximization. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 3:1-3:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ali_et_al:LIPIcs.SEA.2026.3,
  author =	{Ali, Dildar and Jasrotia, Ansh and Salaria, Abishek and Banerjee, Suman},
  title =	{{Approximation Algorithms for Budget Splitting in Multi-Channel Influence Maximization}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{3:1--3:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-422-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{371},
  editor =	{Aum\"{u}ller, Martin and Finocchi, Irene},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2026.3},
  URN =		{urn:nbn:de:0030-drops-260070},
  doi =		{10.4230/LIPIcs.SEA.2026.3},
  annote =	{Keywords: Advertisement, Billboard, Social Network, Bi-submodularity, Influence Maximization}
}

Document

DOI: 10.4230/LIPIcs.SEA.2026.26

Engineering Algorithms for Dynamic Greedy Set Cover

Authors: Amitai Uzrad

Published in: LIPIcs, Volume 371, 24th International Symposium on Experimental Algorithms (SEA 2026)

Abstract

In the dynamic set cover problem, the input is a dynamic universe of elements and a fixed collection of sets. As elements are inserted or deleted, the goal is to efficiently maintain an approximate minimum set cover. While the past decade has seen significant theoretical breakthroughs for this problem, a notable gap remains between theoretical design and practical performance, as no comprehensive experimental study currently exists to validate these results. In this paper, we bridge this gap by implementing and evaluating four greedy-based dynamic algorithms across a diverse range of real-world instances. We derive our implementations from state-of-the-art frameworks - such as [GKKP(STOC'17); SU(STOC'23); SUZ(FOCS'24)] - which we simplify by identifying and modifying intricate subroutines that optimize asymptotic bounds but hinder practical performance. We evaluate these algorithms based on solution quality (set cover size) and efficiency, which comprises update time - the time required to update the solution following each insertion/deletion - and recourse - the number of changes made to the solution per update. Each algorithm uses a parameter β to balance quality against efficiency; we investigate the influence of this tradeoff parameter on each algorithm and then perform a comparative analysis to evaluate the algorithms against each other. Our results provide the first practical insights into which algorithmic strategies provide the most value in realistic scenarios.

Cite as

Amitai Uzrad. Engineering Algorithms for Dynamic Greedy Set Cover. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 26:1-26:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{uzrad:LIPIcs.SEA.2026.26,
  author =	{Uzrad, Amitai},
  title =	{{Engineering Algorithms for Dynamic Greedy Set Cover}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{26:1--26:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-422-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{371},
  editor =	{Aum\"{u}ller, Martin and Finocchi, Irene},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2026.26},
  URN =		{urn:nbn:de:0030-drops-260308},
  doi =		{10.4230/LIPIcs.SEA.2026.26},
  annote =	{Keywords: Dynamic graphs, set cover, recourse}
}

Document

DOI: 10.4230/LIPIcs.SWAT.2026.15

One Color Makes All the Difference in the Tractability of Partial Coloring in Semi-Streaming

Authors: Avinandan Das

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract

This paper investigates the semi-streaming complexity of k-partial coloring, a generalization of proper graph coloring. For k ≥ 1, a k-partial coloring requires that each vertex v in an n-node graph is assigned a color such that at least min{k, deg(v)} of its neighbors are assigned colors different from its own. This framework naturally extends classical coloring problems: specifically, k-partial (k+1)-coloring and k-partial k-coloring generalize (Δ+1)-proper coloring and Δ-proper coloring, respectively. Prior works of Assadi, Chen, and Khanna [SODA 2019] and Assadi, Kumar, and Mittal [TheoretiCS 2023] show that both (Δ+1)-proper coloring and Δ-proper coloring admit one-pass randomized semi-streaming algorithms. We explore whether these efficiency gains extend to their partial coloring generalizations and reveal a sharp computational threshold: while k-partial (k+1)-coloring admits a one-pass randomized semi-streaming algorithm, the k-partial k-coloring remains semi-streaming intractable, effectively demonstrating a "dichotomy of one color" in the streaming model.

Cite as

Avinandan Das. One Color Makes All the Difference in the Tractability of Partial Coloring in Semi-Streaming. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 15:1-15:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{das:LIPIcs.SWAT.2026.15,
  author =	{Das, Avinandan},
  title =	{{One Color Makes All the Difference in the Tractability of Partial Coloring in Semi-Streaming}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{15:1--15:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.15},
  URN =		{urn:nbn:de:0030-drops-260515},
  doi =		{10.4230/LIPIcs.SWAT.2026.15},
  annote =	{Keywords: Graph Coloring, Semi-streaming algorithms, Lower bounds}
}

Document

DOI: 10.4230/LIPIcs.SWAT.2026.16

Online Hitting Set for Axis-Aligned Squares

Authors: Minati De, Satyam Singh, and Csaba D. Tóth

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract

Given a set P of n points in the plane and a sequence of axis-aligned squares that arrive in an online fashion, the online hitting set problem consists of maintaining, by adding new points from P if necessary, a hitting set H ⊆ P, which contains at least one point in every input square that has already arrived. We present an O(log n)-competitive deterministic algorithm for this problem. The competitive ratio is the best possible, apart from constant factors. In fact, this is the first O(log n)-competitive algorithm for the online hitting set problem that works for geometric objects of arbitrary sizes (i.e., unbounded scaling factors) in the plane. We further generalize this result to positive homothets of a polygon with k ≥ 3 vertices in the plane and provide an O(k²log n)-competitive algorithm.

Cite as

Minati De, Satyam Singh, and Csaba D. Tóth. Online Hitting Set for Axis-Aligned Squares. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{de_et_al:LIPIcs.SWAT.2026.16,
  author =	{De, Minati and Singh, Satyam and T\'{o}th, Csaba D.},
  title =	{{Online Hitting Set for Axis-Aligned Squares}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{16:1--16:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.16},
  URN =		{urn:nbn:de:0030-drops-260528},
  doi =		{10.4230/LIPIcs.SWAT.2026.16},
  annote =	{Keywords: axis-aligned squares, hitting set, homothets of a polygon, online algorithm}
}

Document

DOI: 10.4230/LIPIcs.SWAT.2026.26

On the Parameterized Complexity of Min-Sum-Radii

Authors: Pankaj Kumar, Haiko Müller, Sebastian Ordyniak, and Melanie Schmidt

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract

In the Min-Sum-Radii (MSR) clustering problem, we are given a finite set X of n points in a metric space. The objective is to find at most k clusters centered at a subset of these points such that every point of X is assigned to one of the clusters, minimizing the sum of the radii of the clusters. The problem is known to be NP-hard even on metrics induced by weighted planar graphs and metrics with constant doubling dimension, as shown by Gibson et al. (SWAT 2008). In this work, we investigate the parameterized complexity of MSR on metrics induced by undirected graphs. We distinguish between weighted graph metrics (with positive edge weights) and unweighted graph metrics (where all edges have unit weight). Weighted Graph Metrics. We show that MSR is W[1]-hard on metrics induced by weighted bipartite graphs, when parameterized by the combined parameter k the number of clusters and Δ the cost of the clustering. We then investigate the structural parameterized complexity of the problem. Drexler et al. [doi:10.48550/arXiv.2310.02130] showed that the MSR problem admits an XP algorithm on metrics induced by weighted graphs when parameterized by treewidth, and asked whether this can be improved to fixed-parameter tractability. We first answer their question in the negative, and more strongly show that MSR stays W[1]-hard on metrics induced by undirected weighted bipartite graphs when parameterized by the vertex cover number plus k. We then turn our attention to parameters for dense graphs and show that MSR remains W[1]-hard when parameterized by k+Δ even on cliques and complete bipartite graphs. On the positive side, we employ the known XP algorithm parameterized by treewidth, to show that the MSR problem is FPT when parameterized by the parameter treewidth plus Δ. Together, these results provide a complete picture of the parameterized complexity of MSR with respect to any combination of parameters k, Δ, as well as structural parameters for sparse graphs above vertex cover and known parameters for dense graphs (such as neighborhood diversity and modular width). Unweighted Graph Metrics. The story is rather different for unweighted graphs, since it is a long standing open question whether MSR on metrics induced by undirected graphs is solvable in polynomial-time. Although we cannot answer this question, we provide classical and parameterized hardness results for two very closely related problems, namely Exact-MSR (MSR and one wants to find exactly k clusters) and Allowed-Centers-MSR (MSR with an additional set of allowed cluster centers). We also show that MSR as well as these two problems are fixed-parameter tractable parameterized by the treedepth of the input graph.

Cite as

Pankaj Kumar, Haiko Müller, Sebastian Ordyniak, and Melanie Schmidt. On the Parameterized Complexity of Min-Sum-Radii. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 26:1-26:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kumar_et_al:LIPIcs.SWAT.2026.26,
  author =	{Kumar, Pankaj and M\"{u}ller, Haiko and Ordyniak, Sebastian and Schmidt, Melanie},
  title =	{{On the Parameterized Complexity of Min-Sum-Radii}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{26:1--26:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.26},
  URN =		{urn:nbn:de:0030-drops-260623},
  doi =		{10.4230/LIPIcs.SWAT.2026.26},
  annote =	{Keywords: Parameterized complexity, Min-Sum-Radii clustering}
}

Document

DOI: 10.4230/LIPIcs.SWAT.2026.32

Semirandom Planted Bipartite Subgraphs

Authors: Anand Louis and Kirtan Vora

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract

There have been many recent works studying planted subgraphs problems. The semirandom planted bipartite subgraph problem is defined as follows. Starting with a vertex set V, an arbitrary subset S ⊂ V of size k is chosen, then an arbitrary bipartite graph is added on S. After this between each pair of vertices in S × (V ⧵ S) an edge is added independently with probability p, then an arbitrary graph is added on V⧵ S. The analogous semirandom planted clique problem, where S forms a clique, has been studied starting with the work of Fiege and Kilian [Uriel Feige and Joe Kilian, 2001]; recent work by [Blasiok et al., 2024; Venkatesan Guruswami and Hsin-Po Wang, 2025] gave an algorithm for this problem when k = Ω(√{n log n}). We give an algorithm for semirandom planted bipartite subgraph problem when k = Ω(√{n log n}) and the two color classes are roughly balanced. Our algorithms are essentially the same as the elegant greedy algorithm of [Blasiok et al., 2024]. We generalize their idea to our setting. Handling the arbitrary nature of the bipartite graph requires some new technical ideas and is our main technical contribution.

Cite as

Anand Louis and Kirtan Vora. Semirandom Planted Bipartite Subgraphs. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 32:1-32:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{louis_et_al:LIPIcs.SWAT.2026.32,
  author =	{Louis, Anand and Vora, Kirtan},
  title =	{{Semirandom Planted Bipartite Subgraphs}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{32:1--32:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.32},
  URN =		{urn:nbn:de:0030-drops-260681},
  doi =		{10.4230/LIPIcs.SWAT.2026.32},
  annote =	{Keywords: Semirandom Models, Spectral Algorithms, Planted Subgraphs, Random Graphs, Approximate Recovery Algorithms}
}

Document

DOI: 10.4230/LIPIcs.FORC.2026.9

Serving Clients Fairly: On Facility Location and k-Median with Fair Outliers

Authors: Rajni Dabas, Samir Khuller, and Emilie Rivkin

Published in: LIPIcs, Volume 368, 7th Symposium on Foundations of Responsible Computing (FORC 2026)

Abstract

Classical clustering problems such as Facility Location and k-Median aim to efficiently serve a set of clients from a subset of facilities - minimizing the total cost of facility openings and client assignments in Facility Location, and minimizing assignment (service) cost under a facility count constraint in k-Median. These problems are highly sensitive to outliers, and therefore researchers have studied variants that allow excluding a small number of clients as outliers to reduce cost. However, in many real-world settings, clients belong to different demographic or functional groups, and unconstrained outlier removal can disproportionately exclude certain groups, raising fairness concerns, especially when the facilities correspond to critically needed facilities for emergencies such as fire stations, hospitals and other emergency services. We study Facility Location with Fair Outliers, where each group is allowed a specified number of outliers, and the objective is to minimize total cost while respecting group-wise fairness constraints. We present a bicriteria approximation with a O(1/ε) approximation factor and (1+ 2ε) factor violation in outliers per group. For k-Median with Fair Outliers, we design a bicriteria approximation with a 4(1+ω/ε) approximation factor and (ω + ε) violation in outliers per group improving on prior work by avoiding dependence on k in outlier violations. We also prove that the problems are W[1]-hard parameterized by ω. We complement our algorithmic contributions with a detailed empirical analysis, demonstrating that fairness can be achieved with negligible increase in cost and that the integrality gap of the standard LP is small in practice.

Cite as

Rajni Dabas, Samir Khuller, and Emilie Rivkin. Serving Clients Fairly: On Facility Location and k-Median with Fair Outliers. In 7th Symposium on Foundations of Responsible Computing (FORC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 368, pp. 9:1-9:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{dabas_et_al:LIPIcs.FORC.2026.9,
  author =	{Dabas, Rajni and Khuller, Samir and Rivkin, Emilie},
  title =	{{Serving Clients Fairly: On Facility Location and k-Median with Fair Outliers}},
  booktitle =	{7th Symposium on Foundations of Responsible Computing (FORC 2026)},
  pages =	{9:1--9:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-419-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{368},
  editor =	{Lin, Huijia (Rachel)},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2026.9},
  URN =		{urn:nbn:de:0030-drops-259812},
  doi =		{10.4230/LIPIcs.FORC.2026.9},
  annote =	{Keywords: Approximation algorithms, fairness}
}

Document

DOI: 10.4230/LIPIcs.FORC.2026.14

Fair Multi-Agent Persuasion with Submodular Constraints

Authors: Yannan Bai, Kamesh Munagala, Yiheng Shen, and Davidson Zhu

Published in: LIPIcs, Volume 368, 7th Symposium on Foundations of Responsible Computing (FORC 2026)

Abstract

We study the problem of selection in the context of Bayesian persuasion. We are given multiple agents with hidden values (or quality scores), to whom resources must be allocated by a welfare-maximizing decision-maker. An intermediary with knowledge of the agents' values seeks to influence the outcome of the selection by designing informative signals and providing tie-breaking policies, so that when the receiver maximizes welfare over the resulting posteriors, the expected utilities of the agents (where utility is defined as allocation times value) achieve certain fairness properties. The fairness measure we will use is majorization, which simultaneously approximately maximizes all symmetric, monotone, concave functions of the utilities. We consider the general setting where the allocation to the agents needs to respect arbitrary submodular constraints, as given by the corresponding polymatroid. We present a signaling policy that achieves a logarithmically approximate majorized policy in this setting, assuming the receiver is a (1+ε) approximate welfare maximizer. The approximation ratio is almost best possible, and that significantly outperforms generic results that only yield linear approximations. A key component of our result is a structural characterization showing that the vector of agent utilities for a given signaling policy defines the base polytope of a different polymatroid, a result that may be of independent interest. In addition, we show that an arbitrarily good additive approximation to this vector can be produced in (weakly) polynomial time via the multiplicative weights update method.

Cite as

Yannan Bai, Kamesh Munagala, Yiheng Shen, and Davidson Zhu. Fair Multi-Agent Persuasion with Submodular Constraints. In 7th Symposium on Foundations of Responsible Computing (FORC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 368, pp. 14:1-14:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bai_et_al:LIPIcs.FORC.2026.14,
  author =	{Bai, Yannan and Munagala, Kamesh and Shen, Yiheng and Zhu, Davidson},
  title =	{{Fair Multi-Agent Persuasion with Submodular Constraints}},
  booktitle =	{7th Symposium on Foundations of Responsible Computing (FORC 2026)},
  pages =	{14:1--14:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-419-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{368},
  editor =	{Lin, Huijia (Rachel)},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2026.14},
  URN =		{urn:nbn:de:0030-drops-259872},
  doi =		{10.4230/LIPIcs.FORC.2026.14},
  annote =	{Keywords: Bayesian Persuasion, Fair Division, Submodular Optimization}
}

Document

DOI: 10.4230/LIPIcs.SoCG.2026.33

Near-Optimal Bounds for Parameterized Euclidean k-Means

Authors: Vincent Cohen-Addad, Karthik C. S., David Saulpic, and Chris Schwiegelshohn

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract

The k-means problem is a classic objective for modeling clustering in a metric space. Given a set of points in a metric space, the goal is to find k representative points so as to minimize the sum of the squared distances from each point to its closest representative. In this work, we study the approximability of k-means in Euclidean spaces parameterized by the number of clusters, k. In seminal works, de la Vega, Karpinski, Kenyon, and Rabani [STOC'03] and Kumar, Sabharwal, and Sen [JACM'10] showed how to obtain a (1+ε)-approximation for high-dimensional Euclidean k-means in time 2^{(k/ε)^O(1)} ⋅ dn^O(1). In this work, we introduce a new fine-grained hypothesis called Exponential Time for Expanders Hypothesis (XXH) which roughly asserts that there are no non-trivial exponential time approximation algorithms for the vertex cover problem on near perfect vertex expanders. Assuming XXH, we close the above long line of work on approximating Euclidean k-means by showing that there is no 2^{(k/ε)^{1-o(1)}} ⋅ n^O(1) time algorithm achieving a (1+ε)-approximation for k-means in Euclidean space. This lower bound is tight as it matches the algorithm given by Feldman, Monemizadeh, and Sohler [SoCG'07] whose runtime is 2^O(k/ε) + O(ndk). Furthermore, assuming XXH, we show that the seminal O(n^{kd+1}) runtime exact algorithm of Inaba, Katoh, and Imai [SoCG'94] for k-means is optimal for small values of k.

Cite as

Vincent Cohen-Addad, Karthik C. S., David Saulpic, and Chris Schwiegelshohn. Near-Optimal Bounds for Parameterized Euclidean k-Means. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 33:1-33:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{cohenaddad_et_al:LIPIcs.SoCG.2026.33,
  author =	{Cohen-Addad, Vincent and C. S., Karthik and Saulpic, David and Schwiegelshohn, Chris},
  title =	{{Near-Optimal Bounds for Parameterized Euclidean k-Means}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{33:1--33:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.33},
  URN =		{urn:nbn:de:0030-drops-258391},
  doi =		{10.4230/LIPIcs.SoCG.2026.33},
  annote =	{Keywords: k-means clustering, Euclidean space, Fine-Grained Complexity}
}

Document

DOI: 10.4230/LIPIcs.SoCG.2026.34

Almost-Optimal Upper and Lower Bounds for Clustering in Low Dimensional Euclidean Spaces

Authors: Vincent Cohen-Addad, Karthik C. S., David Saulpic, and Chris Schwiegelshohn

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract

The k-median and k-means clustering objectives are classic objectives for modeling clustering in a metric space. Given a set of points in a metric space, the goal of the k-median (resp. k-means) problem is to find k representative points so as to minimize the sum of the distances (resp. sum of squared distances) from each point to its closest representative. Cohen-Addad, Feldmann, and Saulpic [JACM'21] showed how to obtain a (1+ε)-factor approximation in low-dimensional Euclidean metric for both the k-median and k-means problems in near-linear time 2^{(1/ε)^O(d²)} n ⋅ polylog(n) (where d is the dimension and n is the number of input points). We improve this running time to 2^{O(1/ε)^{d-1}} ⋅ n ⋅ polylog(n), and show an almost matching lower bound: under the Gap Exponential Time Hypothesis for 3-SAT, there is no 2^o(1/ε^{d-1}) n^O(1) algorithm achieving a (1+ε)-approximation for k-means.

Cite as

Vincent Cohen-Addad, Karthik C. S., David Saulpic, and Chris Schwiegelshohn. Almost-Optimal Upper and Lower Bounds for Clustering in Low Dimensional Euclidean Spaces. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 34:1-34:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{cohenaddad_et_al:LIPIcs.SoCG.2026.34,
  author =	{Cohen-Addad, Vincent and Karthik C. S. and Saulpic, David and Schwiegelshohn, Chris},
  title =	{{Almost-Optimal Upper and Lower Bounds for Clustering in Low Dimensional Euclidean Spaces}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{34:1--34:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.34},
  URN =		{urn:nbn:de:0030-drops-258404},
  doi =		{10.4230/LIPIcs.SoCG.2026.34},
  annote =	{Keywords: k-means clustering, k-median clustering, Euclidean space, Fine-Grained Complexity}
}

Document

DOI: 10.4230/LIPIcs.SoCG.2026.48

FPT Approximations for Capacitated Sum of Radii and Diameters

Authors: Arnold Filtser and Ameet Gadekar

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract

The Capacitated Sum of Radii problem involves partitioning a set of points P, where each point p ∈ P has capacity U_p, into k clusters that minimize the sum of cluster radii, such that the number of points in the cluster centered at point p is at most U_p. We begin by showing that the problem is APX-hard, and that under gap-ETH there is no parameterized approximation scheme (FPT-AS). We then construct a ≈5.83-approximation algorithm in FPT time (improving a previous ≈7.61 approximation in FPT time). Our results also hold when the objective is a general monotone symmetric norm of radii. We also improve the approximation factors for the uniform capacity case, and for the closely related problem of Capacitated Sum of Diameters.

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Arnold Filtser and Ameet Gadekar. FPT Approximations for Capacitated Sum of Radii and Diameters. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 48:1-48:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{filtser_et_al:LIPIcs.SoCG.2026.48,
  author =	{Filtser, Arnold and Gadekar, Ameet},
  title =	{{FPT Approximations for Capacitated Sum of Radii and Diameters}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{48:1--48:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.48},
  URN =		{urn:nbn:de:0030-drops-258545},
  doi =		{10.4230/LIPIcs.SoCG.2026.48},
  annote =	{Keywords: clustering, sum of radii, sum of diameter, capacitated clustering, fpt}
}

Document

DOI: 10.4230/LIPIcs.SoCG.2026.14

Improved Online Hitting Set Algorithms for Structured and Geometric Set Systems

Authors: Sujoy Bhore, Anupam Gupta, and Amit Kumar

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract

In the online hitting set problem, sets arrive over time, and the algorithm has to maintain a subset of elements that hit all the sets seen so far. Alon, Awerbuch, Azar, Buchbinder, and Naor (SICOMP 2009) gave an algorithm with competitive ratio O(log n log m) for the (general) online hitting set and set cover problems for m sets and n elements; this is known to be tight for efficient online algorithms. Given this barrier for general set systems, we ask: can we break this double-logarithmic phenomenon for online hitting set/set cover on structured and geometric set systems? We provide an O(log n log log n)-competitive algorithm for the weighted online hitting set problem on set systems with linear shallow-cell complexity, replacing the double-logarithmic factor in the general result by effectively a single logarithmic term. As a consequence of our results we obtain the first bounds for weighted online hitting set for natural geometric set families, thereby answering open questions regarding the gap between general and geometric weighted online hitting set problems.

Cite as

Sujoy Bhore, Anupam Gupta, and Amit Kumar. Improved Online Hitting Set Algorithms for Structured and Geometric Set Systems. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 14:1-14:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bhore_et_al:LIPIcs.SoCG.2026.14,
  author =	{Bhore, Sujoy and Gupta, Anupam and Kumar, Amit},
  title =	{{Improved Online Hitting Set Algorithms for Structured and Geometric Set Systems}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{14:1--14:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.14},
  URN =		{urn:nbn:de:0030-drops-258206},
  doi =		{10.4230/LIPIcs.SoCG.2026.14},
  annote =	{Keywords: Hitting Set, Online Algorithms, Shallow-Cell Complexity, VC-Dimension}
}

Document

Research

DOI: 10.4230/TGDK.4.1.4

Native Provenance Computation for Federated and Non-Federated SPARQL Queries

Authors: Zubaria Asma, Daniel Hernández, Luis Galárraga, Giorgos Flouris, Irini Fundulaki, and Katja Hose

Published in: TGDK, Volume 4, Issue 1 (2026). Transactions on Graph Data and Knowledge, Volume 4, Issue 1

Abstract

The popularity of knowledge graphs (KGs) owes credit to their flexible data model, which is suitable for data integration from multiple sources. Several KG-based applications, such as trust assessment, view maintenance, or data valuation on dynamic data, rely on the ability to compute provenance explanations for query results. This need becomes more urgent in federated query processing systems, which allow the online consumption of heterogeneous and decentralized Web data. However, the problem of computing and interacting with provenance has received little attention, especially in the federated setting. On those grounds, this paper introduces the NPCS (Native Provenance Computation for SPARQL) approach, and its federated variant Fed-NPCS, that compute provenance for SPARQL query results. Both approaches build upon spm-semirings to annotate the results of monotonic and non-monotonic SPARQL queries with their provenance. Due to their reliance on query rewriting techniques, the approaches are directly applicable to already deployed SPARQL engines and federations using different reification schemes, including RDF-star. Our experimental evaluation shows that our novel query rewriting approach brings significant run-time improvements w.r.t. the state-of-the-art across both centralized and federated settings. In centralized settings, our tests on two popular SPARQL engines (GraphDB and Stardog) reveal substantial runtime gains over existing query rewriting solutions, enabling scalability to RDF graphs with billions of triples. In federated settings, our experiments on the FedShop benchmark with GraphDB show the viability of Fed-NPCS for federations with up to 200 sources.

Cite as

Zubaria Asma, Daniel Hernández, Luis Galárraga, Giorgos Flouris, Irini Fundulaki, and Katja Hose. Native Provenance Computation for Federated and Non-Federated SPARQL Queries. In Transactions on Graph Data and Knowledge (TGDK), Volume 4, Issue 1, pp. 4:1-4:43, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@Article{asma_et_al:TGDK.4.1.4,
  author =	{Asma, Zubaria and Hern\'{a}ndez, Daniel and Gal\'{a}rraga, Luis and Flouris, Giorgos and Fundulaki, Irini and Hose, Katja},
  title =	{{Native Provenance Computation for Federated and Non-Federated SPARQL Queries}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{4:1--4:43},
  ISSN =	{2942-7517},
  year =	{2026},
  volume =	{4},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.4.1.4},
  URN =		{urn:nbn:de:0030-drops-259642},
  doi =		{10.4230/TGDK.4.1.4},
  annote =	{Keywords: native provenance computation, federated SPARQL queries, data provenance, NPCS, Fed-NPCS}
}

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