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Documents authored by Farokhnejad, Ermiya

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.62
Deterministic k-Median Clustering in Near-Optimal Time

Authors: Martín Costa and Ermiya Farokhnejad

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

Abstract
The metric k-median problem is a textbook clustering problem. As input, we are given a metric space V of size n and an integer k, and our task is to find a subset S ⊆ V of at most k "centers" that minimizes the total distance from each point in V to its nearest center in S. Mettu and Plaxton [UAI'02] gave a randomized algorithm for k-median that computes a O(1)-approximation in Õ(nk) time. They also showed that any algorithm for this problem with a bounded approximation ratio must have a running time of Ω(nk). Thus, the running time of their algorithm is optimal up to polylogarithmic factors. For deterministic k-median, Guha et al. [FOCS'00] gave an algorithm that computes a poly(log (n/k))-approximation in Õ(nk) time, where the degree of the polynomial in the approximation is unspecified. To the best of our knowledge, this remains the state-of-the-art approximation of any deterministic k-median algorithm with this running time. This leads us to the following natural question: What is the best approximation of a deterministic k-median algorithm with near-optimal running time? We make progress in answering this question by giving a deterministic algorithm that computes a O(log(n/k))-approximation in Õ(nk) time. We also provide a lower bound showing that any deterministic algorithm with this running time must have an approximation ratio of Ω(log n/(log k + log log n)), establishing a gap between the randomized and deterministic settings for k-median.
Cite as

Martín Costa and Ermiya Farokhnejad. Deterministic k-Median Clustering in Near-Optimal Time. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 62:1-62:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{costa_et_al:LIPIcs.ICALP.2025.62,
  author =	{Costa, Mart{\'\i}n and Farokhnejad, Ermiya},
  title =	{{Deterministic k-Median Clustering in Near-Optimal Time}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{62:1--62:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.62},
  URN =		{urn:nbn:de:0030-drops-234395},
  doi =		{10.4230/LIPIcs.ICALP.2025.62},
  annote =	{Keywords: k-clustering, k-median, deterministic algorithms, approximation algorithms}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.9
Improved Approximation Algorithms for (1,2)-TSP and Max-TSP Using Path Covers in the Semi-Streaming Model

Authors: Sharareh Alipour, Ermiya Farokhnejad, and Tobias Mömke

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

Abstract
We investigate semi-streaming algorithms for the Traveling Salesman Problem (TSP). Specifically, we focus on a variant known as the (1,2)-TSP, where the distances between any two vertices are either one or two. Our primary emphasis is on the closely related Maximum Path Cover Problem, which aims to find a collection of vertex-disjoint paths that covers the maximum number of edges in a graph. We propose an algorithm that, for any ε > 0, achieves a (2/3-ε)-approximation of the maximum path cover size for an n-vertex graph, using poly(1/ε) passes. This result improves upon the previous 1/2-approximation by Behnezhad et al. [Soheil Behnezhad et al., 2023] in the semi-streaming model. Building on this result, we design a semi-streaming algorithm that constructs a tour for an instance of (1,2)-TSP with an approximation factor of (4/3 + ε), improving upon the previous 3/2-approximation factor algorithm by Behnezhad et al. [Soheil Behnezhad et al., 2023]. Furthermore, we extend our approach to develop an approximation algorithm for the Maximum TSP (Max-TSP), where the goal is to find a Hamiltonian cycle with the maximum possible weight in a given weighted graph G. Our algorithm provides a (7/12 - ε)-approximation for Max-TSP in poly(1/(ε)) passes, improving on the previously known (1/2-ε)-approximation obtained via maximum weight matching in the semi-streaming model.
Cite as

Sharareh Alipour, Ermiya Farokhnejad, and Tobias Mömke. Improved Approximation Algorithms for (1,2)-TSP and Max-TSP Using Path Covers in the Semi-Streaming Model. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{alipour_et_al:LIPIcs.STACS.2025.9,
  author =	{Alipour, Sharareh and Farokhnejad, Ermiya and M\"{o}mke, Tobias},
  title =	{{Improved Approximation Algorithms for (1,2)-TSP and Max-TSP Using Path Covers in the Semi-Streaming Model}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{9:1--9:17},
  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.2025.9},
  URN =		{urn:nbn:de:0030-drops-228342},
  doi =		{10.4230/LIPIcs.STACS.2025.9},
  annote =	{Keywords: (1,2)-TSP, Max-TSP, Maximum Path Cover, Semi-Streaming Algorithms, Approximation Algorithms, Graph Algorithms}
}
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