2 Search Results for "Berend, Daniel"

Document
DOI: 10.4230/LIPIcs.ITCS.2026.94
Smoothed Analysis of Online Metric Matching with a Single Sample: Beyond Metric Distortion

Authors: Yingxi Li, Ellen Vitercik, and Mingwei Yang

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

Abstract
In the online metric matching problem, n servers and n requests lie in a metric space. Servers are available upfront, and requests arrive sequentially. An arriving request must be matched immediately and irrevocably to an available server, incurring a cost equal to their distance. The goal is to minimize the total matching cost. We study this problem in [0, 1]^d with the Euclidean metric, when servers are adversarial and requests are independently drawn from distinct distributions that satisfy a mild smoothness condition. Our main result is an O(1)-competitive algorithm for d ≠ 2 that requires no distributional knowledge, relying only on a single sample from each request distribution. To our knowledge, this is the first algorithm to achieve an o(log n) competitive ratio for non-trivial metrics beyond the i.i.d. setting. Our approach bypasses the Ω(log n) barrier introduced by probabilistic metric embeddings: instead of analyzing the embedding distortion and the algorithm separately, we directly bound the cost of the algorithm on the target metric space of a simple deterministic embedding. We then combine this analysis with lower bounds on the offline optimum for Euclidean metrics, derived via majorization arguments, to obtain our guarantees.
Cite as

Yingxi Li, Ellen Vitercik, and Mingwei Yang. Smoothed Analysis of Online Metric Matching with a Single Sample: Beyond Metric Distortion. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 94:1-94:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{li_et_al:LIPIcs.ITCS.2026.94,
  author =	{Li, Yingxi and Vitercik, Ellen and Yang, Mingwei},
  title =	{{Smoothed Analysis of Online Metric Matching with a Single Sample: Beyond Metric Distortion}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{94:1--94:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.94},
  URN =		{urn:nbn:de:0030-drops-253815},
  doi =		{10.4230/LIPIcs.ITCS.2026.94},
  annote =	{Keywords: Online algorithm, Metric matching, Competitive analysis, Smoothed analysis}
}
Document
DOI: 10.4230/LIPIcs.SEA.2020.8
Effect of Initial Assignment on Local Search Performance for Max Sat

Authors: Daniel Berend and Yochai Twitto

Published in: LIPIcs, Volume 160, 18th International Symposium on Experimental Algorithms (SEA 2020)

Abstract
In this paper, we explore the correlation between the quality of initial assignments provided to local search heuristics and that of the corresponding final assignments. We restrict our attention to the Max r-Sat problem and to one of the leading local search heuristics - Configuration Checking Local Search (CCLS). We use a tailored version of the Method of Conditional Expectations (MOCE) to generate initial assignments of diverse quality. We show that the correlation in question is significant and long-lasting. Namely, even when we delve deeper into the local search, we are still in the shadow of the initial assignment. Thus, under practical time constraints, the quality of the initial assignment is crucial to the performance of local search heuristics. To demonstrate our point, we improve CCLS by combining it with MOCE. Instead of starting CCLS from random initial assignments, we start it from excellent initial assignments, provided by MOCE. Indeed, it turns out that this kind of initialization provides a significant improvement of this state-of-the-art solver. This improvement becomes more and more significant as the instance grows.
Cite as

Daniel Berend and Yochai Twitto. Effect of Initial Assignment on Local Search Performance for Max Sat. In 18th International Symposium on Experimental Algorithms (SEA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 160, pp. 8:1-8:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{berend_et_al:LIPIcs.SEA.2020.8,
  author =	{Berend, Daniel and Twitto, Yochai},
  title =	{{Effect of Initial Assignment on Local Search Performance for Max Sat}},
  booktitle =	{18th International Symposium on Experimental Algorithms (SEA 2020)},
  pages =	{8:1--8:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-148-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{160},
  editor =	{Faro, Simone and Cantone, Domenico},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2020.8},
  URN =		{urn:nbn:de:0030-drops-120823},
  doi =		{10.4230/LIPIcs.SEA.2020.8},
  annote =	{Keywords: Combinatorial Optimization, Maximum Satisfiability, Local Search, Probabilistic Algorithms}
}
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