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DOI: 10.4230/LIPIcs.APPROX/RANDOM.2026.22

A Configuration-LP Framework for Connected k-Median Clustering

Authors: Kushagra Chatterjee, Rojin Rezvan, and Ali Vakilian

Published in: LIPIcs, Volume 392, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2026)

Abstract

We study the connected k-median clustering problem, a clustering problem that augments the classical k-median objective with connectivity constraints. We focus on the overlapping variant of the problem, where clusters are allowed to share vertices. In addition to a metric space (V,d), the input contains a connected graph G on the same vertex set V of size n. The goal is to select at most k centers C and assign vertices to them so as to minimize the k-median cost (i.e., ∑_{v ∈ V} d(v,C)), subject to the constraint that each cluster induces a connected subgraph of G. Since the metric space and the connectivity graph are independent, the problem is significantly more challenging than standard clustering. Eube et al. [Eube et al., 2025] showed that even the assignment version is Ω(log n)-hard to approximate and gave approximation algorithms with guarantees depending polynomially on k. We develop a configuration-LP-based framework that combines covering LP techniques with a rooted minimum-density oracle. For the assignment version, we obtain an O(log² n)-approximation. For the general version, we develop a bicriteria framework that opens O(klog n) centers while achieving an O(log² n)-approximation in cost.

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Kushagra Chatterjee, Rojin Rezvan, and Ali Vakilian. A Configuration-LP Framework for Connected k-Median Clustering. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 392, pp. 22:1-22:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chatterjee_et_al:LIPIcs.APPROX/RANDOM.2026.22,
  author =	{Chatterjee, Kushagra and Rezvan, Rojin and Vakilian, Ali},
  title =	{{A Configuration-LP Framework for Connected k-Median Clustering}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2026)},
  pages =	{22:1--22:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-449-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{392},
  editor =	{Singh, Mohit and Gur, Tom},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2026.22},
  URN =		{urn:nbn:de:0030-drops-277392},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2026.22},
  annote =	{Keywords: Connected Clustering, k-Median Clustering, Configuration LP}
}

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DOI: 10.4230/LIPIcs.FORC.2022.4

Individually-Fair Auctions for Multi-Slot Sponsored Search

Authors: Shuchi Chawla, Rojin Rezvan, and Nathaniel Sauerberg

Published in: LIPIcs, Volume 218, 3rd Symposium on Foundations of Responsible Computing (FORC 2022)

Abstract

We design fair sponsored search auctions that achieve a near-optimal tradeoff between fairness and quality. Our work builds upon the model and auction design of Chawla and Jagadeesan [Chawla and Jagadeesan, 2022], who considered the special case of a single slot. We consider sponsored search settings with multiple slots and the standard model of click through rates that are multiplicatively separable into an advertiser-specific component and a slot-specific component. When similar users have similar advertiser-specific click through rates, our auctions achieve the same near-optimal tradeoff between fairness and quality as in [Chawla and Jagadeesan, 2022]. When similar users can have different advertiser-specific preferences, we show that a preference-based fairness guarantee holds. Finally, we provide a computationally efficient algorithm for computing payments for our auctions as well as those in previous work, resolving another open direction from [Chawla and Jagadeesan, 2022].

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Shuchi Chawla, Rojin Rezvan, and Nathaniel Sauerberg. Individually-Fair Auctions for Multi-Slot Sponsored Search. In 3rd Symposium on Foundations of Responsible Computing (FORC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 218, pp. 4:1-4:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{chawla_et_al:LIPIcs.FORC.2022.4,
  author =	{Chawla, Shuchi and Rezvan, Rojin and Sauerberg, Nathaniel},
  title =	{{Individually-Fair Auctions for Multi-Slot Sponsored Search}},
  booktitle =	{3rd Symposium on Foundations of Responsible Computing (FORC 2022)},
  pages =	{4:1--4:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-226-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{218},
  editor =	{Celis, L. Elisa},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2022.4},
  URN =		{urn:nbn:de:0030-drops-165272},
  doi =		{10.4230/LIPIcs.FORC.2022.4},
  annote =	{Keywords: algorithmic fairness, advertising auctions, and individual fairness}
}

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Documents authored by Rezvan, Rojin

A Configuration-LP Framework for Connected k-Median Clustering

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Individually-Fair Auctions for Multi-Slot Sponsored Search

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