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Documents authored by Carmel, Amir

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Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2026.49
A Scalable and Unified Framework to Weighted Rank Aggregation

Authors: Amir Carmel, Debarati Das, and Tien-Long Nguyen

Published in: LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)

Abstract
The rank aggregation problem, seeks to combine multiple rank orderings of the same set of candidates into a single consensus ordering. Such problems arise in diverse domains, including web search, employment, college admissions, and voting. In this work we focus on the 1-median objective: given a set of m rankings over [n], the goal is to compute a ranking that minimizes the sum of its distances to all input rankings. We study rank aggregation under several classical distance metrics: Ulam distance, Spearman’s footrule, Hamming distance, and Kendall-tau, as well as their weighted variants. Our contributions begin with a novel unified framework that identifies a key structural property: it suffices to focus on a small subset of rankings (of size three or five), where the corresponding local one-median provides a good approximation to the global median. This principle extends across these distance measures, yielding a general algorithmic framework for weighted rank aggregation. Building on this, we present a new approximation algorithm for rank aggregation under the Ulam distance that scales in the Massively Parallel Computation (MPC) model. Our algorithm computes a (2-α)-approximation, for a constant α > 0, to the 1-median in a constant number of rounds, using local memory sublinear in n (the size of a ranking) and total memory near linear in n. We further design new MPC approximation algorithms for Spearman’s footrule and for the element-weighted variants of Hamming and Kendall-tau distances. For each metric, we obtain a (2-ζ)-approximation, for a constant ζ > 0 (which may differ across metrics), to the 1-median in a constant number of rounds, using local memory sublinear in n and total memory linear or near-linear in n. Moreover, for the Ulam distance, where computing the 1-median is NP-hard [Fischer et al., ESA, 2025], we simplify and strengthen the analysis of Chakraborty et al. [ITCS 2023], obtaining an improved 1.968-approximation that further extends to the weighted setting.
Cite as

Amir Carmel, Debarati Das, and Tien-Long Nguyen. A Scalable and Unified Framework to Weighted Rank Aggregation. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 49:1-49:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{carmel_et_al:LIPIcs.ICALP.2026.49,
  author =	{Carmel, Amir and Das, Debarati and Nguyen, Tien-Long},
  title =	{{A Scalable and Unified Framework to Weighted Rank Aggregation}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{49:1--49:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael 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.2026.49},
  URN =		{urn:nbn:de:0030-drops-264385},
  doi =		{10.4230/LIPIcs.ICALP.2026.49},
  annote =	{Keywords: Rank aggregation, 1-median, Ulam distance, Spearman’s footrule, Kendall-tau, Hamming distance, weighted metrics, Massively Parallel Computation, Gromov product}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.42
Fitting Tree Metrics and Ultrametrics in Data Streams

Authors: Amir Carmel, Debarati Das, Evangelos Kipouridis, and Evangelos Pipis

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

Abstract
Fitting distances to tree metrics and ultrametrics are two widely used methods in hierarchical clustering, primarily explored within the context of numerical taxonomy. Formally, given a positive distance function D: binom(V,2) → ℝ_{>0}, the goal is to find a tree (or an ultrametric) T including all elements of set V, such that the difference between the distances among vertices in T and those specified by D is minimized. Numerical taxonomy was first introduced by Sneath and Sokal [Nature 1962], and since then it has been studied extensively in both biology and computer science. In this paper, we initiate the study of ultrametric and tree metric fitting problems in the semi-streaming model, where the distances between pairs of elements from V (with |V| = n), defined by the function D, can arrive in an arbitrary order. We study these problems under various distance norms; namely the 𝓁₀ objective, which aims to minimize the number of modified entries in D to fit a tree-metric or an ultrametric; the 𝓁₁ objective, which seeks to minimize the total sum of distance errors across all pairs of points in V; and the 𝓁_∞ objective, which focuses on minimizing the maximum error incurred by any entries in D. - Our first result addresses the 𝓁₀ objective. We provide a single-pass polynomial-time Õ(n)-space O(1) approximation algorithm for ultrametrics and prove that no single-pass exact algorithm exists, even with exponential time. - Next, we show that the algorithm for 𝓁₀ implies an O(Δ/δ) approximation for the 𝓁₁ objective, where Δ is the maximum, and δ is the minimum absolute difference between distances in the input. This bound matches the best-known approximation for the RAM model using a combinatorial algorithm when Δ/δ = O(n). - For the 𝓁_∞ objective, we provide a complete characterization of the ultrametric fitting problem. First, we present a single-pass polynomial-time Õ(n)-space 2-approximation algorithm and show that no better than 2-approximation is possible, even with exponential time. Furthermore, we show that with an additional pass, it is possible to achieve a polynomial-time exact algorithm for ultrametrics. - Finally, we extend all these results to tree metrics by using only one additional pass through the stream and without asymptotically increasing the approximation factor.
Cite as

Amir Carmel, Debarati Das, Evangelos Kipouridis, and Evangelos Pipis. Fitting Tree Metrics and Ultrametrics in Data Streams. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 42:1-42:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{carmel_et_al:LIPIcs.ICALP.2025.42,
  author =	{Carmel, Amir and Das, Debarati and Kipouridis, Evangelos and Pipis, Evangelos},
  title =	{{Fitting Tree Metrics and Ultrametrics in Data Streams}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{42:1--42:21},
  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.2025.42},
  URN =		{urn:nbn:de:0030-drops-234197},
  doi =		{10.4230/LIPIcs.ICALP.2025.42},
  annote =	{Keywords: Streaming, Clustering, Ultrametrics, Tree metrics, Distance fitting}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.28
Coresets for 1-Center in 𝓁₁ Metrics

Authors: Amir Carmel, Chengzhi Guo, Shaofeng H.-C. Jiang, and Robert Krauthgamer

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
We explore the applicability of coresets - a small subset of the input dataset that approximates a predefined set of queries - to the 1-center problem in 𝓁₁ spaces. This approach could potentially extend to solving the 1-center problem in related metric spaces, and has implications for streaming and dynamic algorithms. We show that in 𝓁₁, unlike in Euclidean space, even weak coresets exhibit exponential dependency on the underlying dimension. Moreover, while inputs with a unique optimal center admit better bounds, they are not dimension independent. We then relax the guarantee of the coreset further, to merely approximate the value (optimal cost of 1-center), and obtain a dimension-independent coreset for every desired accuracy ε > 0. Finally, we discuss the broader implications of our findings to related metric spaces, and show explicit implications to Jaccard and Kendall’s tau distances.
Cite as

Amir Carmel, Chengzhi Guo, Shaofeng H.-C. Jiang, and Robert Krauthgamer. Coresets for 1-Center in 𝓁₁ Metrics. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 28:1-28:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{carmel_et_al:LIPIcs.ITCS.2025.28,
  author =	{Carmel, Amir and Guo, Chengzhi and Jiang, Shaofeng H.-C. and Krauthgamer, Robert},
  title =	{{Coresets for 1-Center in 𝓁₁ Metrics}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{28:1--28:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.28},
  URN =		{urn:nbn:de:0030-drops-226566},
  doi =		{10.4230/LIPIcs.ITCS.2025.28},
  annote =	{Keywords: clustering, k-center, minimum enclosing balls, coresets, 𝓁₁ norm, Kendall’s tau, Jaccard metric}
}
Document
DOI: 10.4230/LIPIcs.CPM.2016.17
On Almost Monge All Scores Matrices

Authors: Amir Carmel, Dekel Tsur, and Michal Ziv-Ukelson

Published in: LIPIcs, Volume 54, 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)

Abstract
The all scores matrix of a grid graph is a matrix containing the optimal scores of paths from every vertex on the first row of the graph to every vertex on the last row. This matrix is commonly used to solve diverse string comparison problems. All scores matrices have the Monge property, and this was exploited by previous works that used all scores matrices for solving various problems. In this paper, we study an extension of grid graphs that contain an additional set of edges, called bridges. Our main result is to show several properties of the all scores matrices of such graphs. We also give an O(r(nm + n2)) time algorithm for constructing the all scores matrix of an m × n grid graph with r bridges.
Cite as

Amir Carmel, Dekel Tsur, and Michal Ziv-Ukelson. On Almost Monge All Scores Matrices. In 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 54, pp. 17:1-17:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{carmel_et_al:LIPIcs.CPM.2016.17,
  author =	{Carmel, Amir and Tsur, Dekel and Ziv-Ukelson, Michal},
  title =	{{On Almost Monge All Scores Matrices}},
  booktitle =	{27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)},
  pages =	{17:1--17:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-012-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{54},
  editor =	{Grossi, Roberto and Lewenstein, Moshe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2016.17},
  URN =		{urn:nbn:de:0030-drops-60770},
  doi =		{10.4230/LIPIcs.CPM.2016.17},
  annote =	{Keywords: Sequence alignment, longest common subsequences, DIST matrices, Monge matrices, all path score computations.}
}
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