27 Search Results for "Kumar, Rohit"

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.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.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.
Cite as

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/OASIcs.NINeS.2026.19
Simulate Before Sending: Rethinking Transport in Datacenter Networks

Authors: Dan Straussman, Isaac Keslassy, Alexander Shpiner, and Liran Liss

Published in: OASIcs, Volume 139, 1st New Ideas in Networked Systems (NINeS 2026)

Abstract
Existing transport protocols in commodity datacenter networks struggle to provide low collective completion times (CCTs) to AI training collectives, as packet losses and retransmissions significantly degrade performance. We propose dcSim, an efficient transport that achieves low CCTs and practically lossless performance with commodity switches. In dcSim, each packet first employs a small simulation probe to traverse the network and explore congestion along a candidate path. Only packets whose simulation probes succeed are then transmitted, expecting to succeed as well. Evaluations confirm that dcSim achieves faster CCTs than existing schemes, with small queues and virtually zero packet loss. Finally, dcSim also excels in adverse conditions, including oversubscribed topologies.
Cite as

Dan Straussman, Isaac Keslassy, Alexander Shpiner, and Liran Liss. Simulate Before Sending: Rethinking Transport in Datacenter Networks. In 1st New Ideas in Networked Systems (NINeS 2026). Open Access Series in Informatics (OASIcs), Volume 139, pp. 19:1-19:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{straussman_et_al:OASIcs.NINeS.2026.19,
  author =	{Straussman, Dan and Keslassy, Isaac and Shpiner, Alexander and Liss, Liran},
  title =	{{Simulate Before Sending: Rethinking Transport in Datacenter Networks}},
  booktitle =	{1st New Ideas in Networked Systems (NINeS 2026)},
  pages =	{19:1--19:22},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-414-7},
  ISSN =	{2190-6807},
  year =	{2026},
  volume =	{139},
  editor =	{Argyraki, Katerina and Panda, Aurojit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.NINeS.2026.19},
  URN =		{urn:nbn:de:0030-drops-256044},
  doi =		{10.4230/OASIcs.NINeS.2026.19},
  annote =	{Keywords: Datacenter networks, transport protocols, AI training, lossless networks}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.45
Fairness in the k-Server Problem

Authors: Mohammadreza Daneshvaramoli, Mohammad Hajiesmaili, Shahin Kamali, Helia Karisani, and Cameron Musco

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

Abstract
We initiate a formal study of fairness for the k-server problem, where the objective is not only to minimize the total movement cost, but also to distribute the cost equitably among servers. We first define a general notion of (α,β)-fairness, where, for parameters α ≥ 1 and β ≥ 0, no server incurs more than an α/k-fraction of the total cost plus an additive term β. We then show that fairness can be achieved without a loss in competitiveness in both the offline and online settings. In the offline setting, we give a deterministic algorithm that, for any ε > 0, transforms any optimal solution into an (α,β)-fair solution for α = 1 + ε and β = O(diam ⋅ log k / ε), while increasing the cost of the solution by just an additive O(diam ⋅ k log k / ε) term. Here diam is the diameter of the underlying metric space. We give a similar result in the online setting, showing that any competitive algorithm can be transformed into a randomized online algorithm that is fair with high probability against an oblivious adversary and still competitive up to a small loss. The above results leave open a significant question: can fairness be achieved in the online setting, either with a deterministic algorithm or a randomized algorithm, against a fully adaptive adversary? We make progress towards answering this question, showing that the classic deterministic Double Coverage Algorithm (DCA) is fair on line metrics and on tree metrics when k = 2. However, we also show a negative result: DCA fails to be fair for any non-vacuous parameters on general tree metrics. We further show that on uniform metrics (i.e., the paging problem), the deterministic First-In First-Out (FIFO) algorithm is fair. We show that any "marking algorithm", including the Least Recently Used (LRU) algorithm, also satisfies a weaker, but still meaningful notion of fairness.
Cite as

Mohammadreza Daneshvaramoli, Mohammad Hajiesmaili, Shahin Kamali, Helia Karisani, and Cameron Musco. Fairness in the k-Server Problem. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 45:1-45:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{daneshvaramoli_et_al:LIPIcs.ITCS.2026.45,
  author =	{Daneshvaramoli, Mohammadreza and Hajiesmaili, Mohammad and Kamali, Shahin and Karisani, Helia and Musco, Cameron},
  title =	{{Fairness in the k-Server Problem}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{45:1--45:21},
  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.2026.45},
  URN =		{urn:nbn:de:0030-drops-253328},
  doi =		{10.4230/LIPIcs.ITCS.2026.45},
  annote =	{Keywords: k-server problem, online algorithms, fairness, competitive analysis}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.49
Debordering Closure Results in Determinantal and Pfaffian Ideals

Authors: Anakin Dey and Zeyu Guo

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

Abstract
One important question in algebraic complexity is understanding the complexity of polynomial ideals (Grochow, Bulletin of EATCS 131, 2020). Andrews and Forbes (STOC 2022) studied the determinantal ideals I^{det}_{n,m,r} generated by the r× r minors of n× m matrices. Over fields of characteristic zero or of sufficiently large characteristic, they showed that for any nonzero f ∈ I^{det}_{n,m,r}, the determinant of a t × t matrix of variables with t = Θ{r^{1/3}} is approximately computed by a constant-depth, polynomial-size f-oracle algebraic circuit, in the sense that the determinant lies in the border of such circuits. An analogous result was also obtained for Pfaffians in the same paper. In this work, we deborder the result of Andrews and Forbes by showing that when f has polynomial degree, the determinant is in fact exactly computed by a constant-depth, polynomial-size f-oracle algebraic circuit. We further establish an analogous result for Pfaffian ideals. Our results are established using the isolation lemma, combined with a careful analysis of straightening-law expansions of polynomials in determinantal and Pfaffian ideals.
Cite as

Anakin Dey and Zeyu Guo. Debordering Closure Results in Determinantal and Pfaffian Ideals. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 49:1-49:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{dey_et_al:LIPIcs.ITCS.2026.49,
  author =	{Dey, Anakin and Guo, Zeyu},
  title =	{{Debordering Closure Results in Determinantal and Pfaffian Ideals}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{49:1--49:24},
  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.2026.49},
  URN =		{urn:nbn:de:0030-drops-253363},
  doi =		{10.4230/LIPIcs.ITCS.2026.49},
  annote =	{Keywords: Algebraic circuit complexity, Isolation lemma, Debordering}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.9
On Closure Properties of Read-Once Oblivious Algebraic Branching Programs

Authors: Robert Andrews, Jules Armand, Prateek Dwivedi, Magnus Rahbek Dalgaard Hansen, Nutan Limaye, Srikanth Srinivasan, and Sébastien Tavenas

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

Abstract
We investigate the closure properties of read-once oblivious Algebraic Branching Programs (roABPs) under various natural algebraic operations and prove the following. - Non-closure under factoring: There is a sequence of explicit polynomials (f_n(x₁,…, x_n))_n that have poly(n)-sized roABPs such that some irreducible factor of f_n requires roABPs of superpolynomial size in any order. - Non-closure under powering: There is a sequence of polynomials (f_n(x₁,…, x_n))_n with poly(n)-sized roABPs such that any super-constant power of f_n does not have roABPs of polynomial size in any order (and f_nⁿ requires exponential size in any order). - Non-closure under symmetric operations: There are symmetric polynomials (f_n(e₁,…, e_n))_n that have roABPs of polynomial size such that f_n(x₁,…, x_n) do not have roABPs of subexponential size. (Here, e₁,…, e_n denote the elementary symmetric polynomials in n variables.) These results should be viewed in light of known results on models such as algebraic circuits, (general) algebraic branching programs, formulas and constant-depth circuits, all of which are known to be closed under these operations. To prove non-closure under factoring, we construct hard polynomials based on expander graphs using gadgets that lift their hardness from sparse polynomials to roABPs. For symmetric compositions, we show that the circulant polynomial requires roABPs of exponential size in every variable order.
Cite as

Robert Andrews, Jules Armand, Prateek Dwivedi, Magnus Rahbek Dalgaard Hansen, Nutan Limaye, Srikanth Srinivasan, and Sébastien Tavenas. On Closure Properties of Read-Once Oblivious Algebraic Branching Programs. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 9:1-9:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{andrews_et_al:LIPIcs.ITCS.2026.9,
  author =	{Andrews, Robert and Armand, Jules and Dwivedi, Prateek and Hansen, Magnus Rahbek Dalgaard and Limaye, Nutan and Srinivasan, Srikanth and Tavenas, S\'{e}bastien},
  title =	{{On Closure Properties of Read-Once Oblivious Algebraic Branching Programs}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{9:1--9:21},
  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.2026.9},
  URN =		{urn:nbn:de:0030-drops-252964},
  doi =		{10.4230/LIPIcs.ITCS.2026.9},
  annote =	{Keywords: Factoring, Closure Properties, Sparsity Bounds, Symmetric Polynomials, roABP, Expander Graphs}
}
Document
Research
DOI: 10.4230/TGDK.3.3.4
Mining Inter-Document Argument Structures in Scientific Papers for an Argument Web

Authors: Florian Ruosch, Cristina Sarasua, and Abraham Bernstein

Published in: TGDK, Volume 3, Issue 3 (2025). Transactions on Graph Data and Knowledge, Volume 3, Issue 3

Abstract
In Argument Mining, predicting argumentative relations between texts (or spans) remains one of the most challenging aspects, even more so in the cross-document setting. This paper makes three key contributions to advance research in this domain. We first extend an existing dataset, the Sci-Arg corpus, by annotating it with explicit inter-document argumentative relations, thereby allowing arguments to be distributed over several documents forming an Argument Web; these new annotations are published using Semantic Web technologies (RDF, OWL). Second, we explore and evaluate three automated approaches for predicting these inter-document argumentative relations, establishing critical baselines on the new dataset. We find that a simple classifier based on discourse indicators with access to context outperforms neural methods. Third, we conduct a comparative analysis of these approaches for both intra- and inter-document settings, identifying statistically significant differences in results that indicate the necessity of distinguishing between these two scenarios. Our findings highlight significant challenges in this complex domain and open crucial avenues for future research on the Argument Web of Science, particularly for those interested in leveraging Semantic Web technologies and knowledge graphs to understand scholarly discourse. With this, we provide the first stepping stones in the form of a benchmark dataset, three baseline methods, and an initial analysis for a systematic exploration of this field relevant to the Web of Data and Science.
Cite as

Florian Ruosch, Cristina Sarasua, and Abraham Bernstein. Mining Inter-Document Argument Structures in Scientific Papers for an Argument Web. In Transactions on Graph Data and Knowledge (TGDK), Volume 3, Issue 3, pp. 4:1-4:33, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@Article{ruosch_et_al:TGDK.3.3.4,
  author =	{Ruosch, Florian and Sarasua, Cristina and Bernstein, Abraham},
  title =	{{Mining Inter-Document Argument Structures in Scientific Papers for an Argument Web}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{4:1--4:33},
  ISSN =	{2942-7517},
  year =	{2025},
  volume =	{3},
  number =	{3},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.3.3.4},
  URN =		{urn:nbn:de:0030-drops-252159},
  doi =		{10.4230/TGDK.3.3.4},
  annote =	{Keywords: Argument Mining, Large Language Models, Knowledge Graphs, Link Prediction}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.19
Clustering in Varying Metrics

Authors: Deeparnab Chakrabarty, Jonathan Conroy, and Ankita Sarkar

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
We introduce the aggregated clustering problem, where one is given T instances of a center-based clustering task over the same n points, but under different metrics. The goal is to open k centers to minimize an aggregate of the clustering costs - e.g., the average or maximum - where the cost is measured via k-center/median/means objectives. More generally, we minimize a norm Ψ over the T cost values. We show that for T ≥ 3, the problem is inapproximable to any finite factor in polynomial time. For T = 2, we give constant-factor approximations. We also show W[2]-hardness when parameterized by k, but obtain f(k,T)poly(n)-time 3-approximations when parameterized by both k and T. When the metrics have structure, we obtain efficient parameterized approximation schemes (EPAS). If all T metrics have bounded ε-scatter dimension, we achieve a (1+ε)-approximation in f(k,T,ε)poly(n) time. If the metrics are induced by edge weights on a common graph G of bounded treewidth tw, and Ψ is the sum function, we get an EPAS in f(T,ε,tw)poly(n,k) time. Conversely, unless (randomized) ETH is false, any finite factor approximation is impossible if parametrized by only T, even when the treewidth is tw = Ω(polylog n).
Cite as

Deeparnab Chakrabarty, Jonathan Conroy, and Ankita Sarkar. Clustering in Varying Metrics. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 19:1-19:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chakrabarty_et_al:LIPIcs.FSTTCS.2025.19,
  author =	{Chakrabarty, Deeparnab and Conroy, Jonathan and Sarkar, Ankita},
  title =	{{Clustering in Varying Metrics}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{19:1--19:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.19},
  URN =		{urn:nbn:de:0030-drops-251007},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.19},
  annote =	{Keywords: Clustering, approximation algorithms, LP rounding, parameterized and exact algorithms, dynamic programming, fixed parameter tractability, hardness of approximation}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.15
Extending EFX Allocations to Further Multi-Graph Classes

Authors: Umang Bhaskar and Yeshwant Pandit

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
The existence of EFX allocations is one of the most significant open questions in fair division. Recent work by Christodoulou, Fiat, Koutsoupias, and Sgouritsa ("Fair allocation in graphs," EC 2023) establishes the existence of EFX allocations for graphical valuations, when agents are vertices in a graph, items are edges, and each item has zero value for all agents other than those at its endpoints. Thus, in this setting, each good has non-zero value for at most two agents, and there is at most one good valued by any pair of agents. This marks one of the few cases when an exact and complete EFX allocation is known to exist for more than three agents. In this work, we partially extend these results to multi-graphs, when each pair of vertices can have more than one edge between them. The existence of EFX allocations in multi-graphs is a natural open question given their existence in simple graphs. We show that EFX allocations exist, and can be computed in polynomial time, for agents with cancelable valuations in the following cases: (i) bipartite multi-graphs, (ii) multi-trees with monotone valuations, and (iii) multi-graphs with girth (2t-1), where t is the chromatic number of the multi-graph. The existence of EFX in cycle multi-graphs follows from (i), (iii), and the known existence of EFX for three agents.
Cite as

Umang Bhaskar and Yeshwant Pandit. Extending EFX Allocations to Further Multi-Graph Classes. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bhaskar_et_al:LIPIcs.FSTTCS.2025.15,
  author =	{Bhaskar, Umang and Pandit, Yeshwant},
  title =	{{Extending EFX Allocations to Further Multi-Graph Classes}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{15:1--15:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.15},
  URN =		{urn:nbn:de:0030-drops-250958},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.15},
  annote =	{Keywords: Fair Division, EFX, Multi-graphs}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.19
On Finding 𝓁-Th Smallest Perfect Matchings

Authors: Nicolas El Maalouly, Sebastian Haslebacher, Adrian Taubner, and Lasse Wulf

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

Abstract
Given an undirected weighted graph G and an integer k, Exact-Weight Perfect Matching (EWPM) is the problem of finding a perfect matching of weight exactly k in G. In this paper, we study EWPM and its variants. The EWPM problem is famous, since in the case of unary encoded weights, Mulmuley, Vazirani, and Vazirani showed almost 40 years ago that the problem can be solved in randomized polynomial time. However, up to this date no derandomization is known. Our first result is a simple deterministic algorithm for EWPM that runs in time n^𝒪(𝓁), where 𝓁 is the number of distinct weights that perfect matchings in G can take. In fact, we show how to find an 𝓁-th smallest perfect matching in any weighted graph (even if the weights are encoded in binary, in which case EWPM in general is known to be NP-complete) in time n^𝒪(𝓁) for any integer 𝓁. Similar next-to-optimal variants have also been studied recently for the shortest path problem. For our second result, we extend the list of problems that are known to be equivalent to EWPM. We show that EWPM is equivalent under a weight-preserving reduction to the Exact Cycle Sum problem (ECS) in undirected graphs with a conservative (i.e. no negative cycles) weight function. To the best of our knowledge, we are the first to study this problem. As a consequence, the latter problem is contained in RP if the weights are encoded in unary. Finally, we identify a special case of EWPM, called BCPM, which was recently studied by El Maalouly, Steiner and Wulf. We show that BCPM is equivalent under a weight-preserving transformation to another problem recently studied by Schlotter and Sebő as well as Geelen and Kapadia: the Shortest Odd Cycle problem (SOC) in undirected graphs with conservative weights. Finally, our n^𝒪(𝓁) algorithm works in this setting as well, identifying a tractable special case of SOC, BCPM, and ECS.
Cite as

Nicolas El Maalouly, Sebastian Haslebacher, Adrian Taubner, and Lasse Wulf. On Finding 𝓁-Th Smallest Perfect Matchings. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 19:1-19:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{elmaalouly_et_al:LIPIcs.ESA.2025.19,
  author =	{El Maalouly, Nicolas and Haslebacher, Sebastian and Taubner, Adrian and Wulf, Lasse},
  title =	{{On Finding 𝓁-Th Smallest Perfect Matchings}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{19:1--19:15},
  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.2025.19},
  URN =		{urn:nbn:de:0030-drops-244875},
  doi =		{10.4230/LIPIcs.ESA.2025.19},
  annote =	{Keywords: Exact Matching, Perfect Matching, Exact-Weight Perfect Matching, Shortest Odd Cycle, Exact Cycle Sum, l-th Smallest Solution, l-th Largest Solution, k-th Best Solution, Derandomization}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.38
Tight Guarantees for Cut-Relative Survivable Network Design via a Decomposition Technique

Authors: Nikhil Kumar, J. J. Nan, and Chaitanya Swamy

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

Abstract
In the classical survivable-network-design problem (SNDP), we are given an undirected graph G = (V, E), non-negative edge costs, and some k tuples (s_i,t_i,r_i), where s_i,t_i ∈ V and r_i ∈ ℤ_+. The objective is to find a minimum-cost subset H ⊆ E such that each s_i-t_i pair remains connected even after the failure of any r_i-1 edges. It is well-known that SNDP can be equivalently modeled using a weakly-supermodular cut-requirement function f, where the objective is to find the minimum-cost subset of edges that picks at least f(S) edges across every cut S ⊆ V. Recently, motivated by fault-tolerance in graph spanners, Dinitz, Koranteng, and Kortsartz proposed a variant of SNDP that enforces a relative level of fault tolerance with respect to G. Even if a feasible SNDP-solution may not exist due to G lacking the required fault-tolerance, the goal is to find a solution H that is at least as fault-tolerant as G itself. They formalize the latter condition in terms of paths and fault-sets, which gives rise to path-relative SNDP (which they call relative SNDP). Along these lines, we introduce a new model of relative network design, called cut-relative SNDP (CR-SNDP), where the goal is to select a minimum-cost subset of edges that satisfies the given (weakly-supermodular) cut-requirement function to the maximum extent possible, i.e., by picking min{f(S), |δ_G(S)|} edges across every cut S ⊆ V. Unlike SNDP, the cut-relative and path-relative versions of SNDP are not equivalent. The resulting cut-requirement function for CR-SNDP (as also path-relative SNDP) is not weakly supermodular, and extreme-point solutions to the natural LP-relaxation need not correspond to a laminar family of tight cut constraints. Consequently, standard techniques cannot be used directly to design approximation algorithms for this problem. We develop a novel decomposition technique to circumvent this difficulty and use it to give a tight 2-approximation algorithm for CR-SNDP. We also show some new hardness results for these relative-SNDP problems.
Cite as

Nikhil Kumar, J. J. Nan, and Chaitanya Swamy. Tight Guarantees for Cut-Relative Survivable Network Design via a Decomposition Technique. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 38:1-38:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kumar_et_al:LIPIcs.ESA.2025.38,
  author =	{Kumar, Nikhil and Nan, J. J. and Swamy, Chaitanya},
  title =	{{Tight Guarantees for Cut-Relative Survivable Network Design via a Decomposition Technique}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{38:1--38:18},
  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.2025.38},
  URN =		{urn:nbn:de:0030-drops-245061},
  doi =		{10.4230/LIPIcs.ESA.2025.38},
  annote =	{Keywords: Approximation algorithms, Network Design, Cut-requirement functions, Weak Supermodularity, Iterative rounding, LP rounding algorithms}
}
Document
DOI: 10.4230/OASIcs.ICPEC.2025.8
RAGent: A Self-Learning RAG Agent for Adaptive Data Science Education

Authors: Mariia Vetluzhskikh and Fardina Fathmiul Alam

Published in: OASIcs, Volume 133, 6th International Computer Programming Education Conference (ICPEC 2025)

Abstract
Undergraduate data science education faces a scalability challenge: addressing a high volume of diverse student questions stemming from varying levels of prior knowledge, technical skills, and learning styles - while ensuring timely and accurate responses. Traditional solutions like manual replies or generic chatbots often fall short in terms of contextual relevance, speed, and efficiency. To tackle this, we introduce RAGent, a Retrieval-Augmented Generation (RAG) agent tailored for a university-level data science course at the University of Maryland. RAGent integrates course-specific materials - lecture notes, assignments, and syllabi - to deliver fast, context-aware answers while maintaining low computational overhead. A central innovation of RAGent is its query classification system, which categorizes student questions into: (i) directly answerable, (ii) relevant but unresolved (requiring instructor input), and (iii) irrelevant or out-of-scope. This system uses semantic similarity, keyword relevance, and dynamic thresholds to drive a targeted prompting strategy, enhancing response accuracy. Another key feature is RAGent’s self-learning loop, which continuously improves performance by integrating resolved queries into its knowledge base and flagging unresolved ones for review and retraining. This dual mechanism ensures both immediate adaptability and long-term scalability. We evaluate RAGent using standard NLP metrics (accuracy, precision, recall, F1-score) and report strong performance in filtering and answering student queries. In a user study with 125 students, over 94% expressed a desire to keep RAGent in the course, citing improved clarity and helpfulness. These results suggest that RAGent significantly enhances support in data science education by providing accurate, contextual responses and reducing instructor workload - offering a scalable, adaptive alternative to conventional support methods. Future work will explore deployment across additional courses and institutions to further validate the RAGent’s adaptability.
Cite as

Mariia Vetluzhskikh and Fardina Fathmiul Alam. RAGent: A Self-Learning RAG Agent for Adaptive Data Science Education. In 6th International Computer Programming Education Conference (ICPEC 2025). Open Access Series in Informatics (OASIcs), Volume 133, pp. 8:1-8:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{vetluzhskikh_et_al:OASIcs.ICPEC.2025.8,
  author =	{Vetluzhskikh, Mariia and Alam, Fardina Fathmiul},
  title =	{{RAGent: A Self-Learning RAG Agent for Adaptive Data Science Education}},
  booktitle =	{6th International Computer Programming Education Conference (ICPEC 2025)},
  pages =	{8:1--8:10},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-393-5},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{133},
  editor =	{Queir\'{o}s, Ricardo and Pinto, M\'{a}rio and Portela, Filipe and Sim\~{o}es, Alberto},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ICPEC.2025.8},
  URN =		{urn:nbn:de:0030-drops-240387},
  doi =		{10.4230/OASIcs.ICPEC.2025.8},
  annote =	{Keywords: RAG, Agent, Chatbot, Data Science, Education, Query Classification, Information Retrieval, LLM}
}
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)

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@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.2025.23
Improved FPT Approximation for Sum of Radii Clustering with Mergeable Constraints

Authors: Sayan Bandyapadhyay and Tianzhi Chen

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

Abstract
In this work, we study k-min-sum-of-radii (k-MSR) clustering under mergeable constraints. k-MSR seeks to group data points using a set of up to k balls, such that the sum of the radii of the balls is minimized. A clustering constraint is called mergeable if merging two clusters satisfying the constraint, results in a cluster that also satisfies the constraint. Many popularly studied constraints are mergeable, including fairness constraints and lower bound constraints. In our work, we design a (4+ε)-approximation for k-MSR under any given mergeable constraint with runtime 2^{O(k/(ε)⋅log²k/ε)} n⁴, i.e., fixed-parameter tractable in k for constant ε. Our result directly improves upon the FPT (6+ε)-approximation by Carta et al. [Carta et al., 2024]. We also provide a hardness result that excludes the exact solvability of k-MSR under any given mergeable constraint in time f(k)n^o(k), assuming ETH is true.
Cite as

Sayan Bandyapadhyay and Tianzhi Chen. Improved FPT Approximation for Sum of Radii Clustering with Mergeable Constraints. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 23:1-23:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bandyapadhyay_et_al:LIPIcs.APPROX/RANDOM.2025.23,
  author =	{Bandyapadhyay, Sayan and Chen, Tianzhi},
  title =	{{Improved FPT Approximation for Sum of Radii Clustering with Mergeable Constraints}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{23:1--23:17},
  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.2025.23},
  URN =		{urn:nbn:de:0030-drops-243894},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.23},
  annote =	{Keywords: sum-of-radii clustering, mergeable constraints, approximation algorithm}
}
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