3 Search Results for "Abdullah, Amirali"

Document
DOI: 10.4230/LIPIcs.ITCS.2026.59
On Approximating the f-Divergence Between Two Ising Models

Authors: Weiming Feng and Yucheng Fu

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

Abstract
The f-divergence is a fundamental notion that measures the difference between two distributions. In this paper, we study the problem of approximating the f-divergence between two Ising models, which is a generalization of recent work on approximating the TV-distance. Given two Ising models ν and μ, which are specified by their interaction matrices and external fields, the problem is to approximate the f-divergence D_f (ν ‖ μ) within an arbitrary relative error e^{±ε}. For χ^α-divergence with a constant integer α, we establish both algorithmic and hardness results. The algorithm works in a parameter regime that matches the hardness result. Our algorithm can be extended to other f-divergences such as α-divergence, Kullback-Leibler divergence, Rényi divergence, Jensen-Shannon divergence, and squared Hellinger distance.
Cite as

Weiming Feng and Yucheng Fu. On Approximating the f-Divergence Between Two Ising Models. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 59:1-59:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{feng_et_al:LIPIcs.ITCS.2026.59,
  author =	{Feng, Weiming and Fu, Yucheng},
  title =	{{On Approximating the f-Divergence Between Two Ising Models}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{59:1--59:23},
  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.2026.59},
  URN =		{urn:nbn:de:0030-drops-253469},
  doi =		{10.4230/LIPIcs.ITCS.2026.59},
  annote =	{Keywords: Ising model, f-divergence, approximation algorithms, randomized algorithms}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.45
Fast Kd-Trees for the Kullback-Leibler Divergence and Other Decomposable Bregman Divergences

Authors: Tuyen Pham and Hubert Wagner

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
The contributions of the paper span theoretical and implementational results. First, we prove that Kd-trees can be extended to ℝ^d with the distance measured by an arbitrary Bregman divergence. Perhaps surprisingly, this shows that the triangle inequality is not necessary for correct pruning in Kd-trees. Second, we offer an efficient algorithm and C++ implementation for nearest neighbour search for decomposable Bregman divergences. The implementation supports the Kullback-Leibler divergence (relative entropy) which is a popular distance between probability vectors and is commonly used in statistics and machine learning. This is a step toward broadening the usage of computational geometry algorithms. Our benchmarks show that our implementation efficiently handles both exact and approximate nearest neighbour queries. Compared to a linear search, we achieve two orders of magnitude speedup for practical scenarios in dimension up to 100. Our solution is simpler and more efficient than competing methods.
Cite as

Tuyen Pham and Hubert Wagner. Fast Kd-Trees for the Kullback-Leibler Divergence and Other Decomposable Bregman Divergences. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 45:1-45:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{pham_et_al:LIPIcs.WADS.2025.45,
  author =	{Pham, Tuyen and Wagner, Hubert},
  title =	{{Fast Kd-Trees for the Kullback-Leibler Divergence and Other Decomposable Bregman Divergences}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{45:1--45:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.45},
  URN =		{urn:nbn:de:0030-drops-242766},
  doi =		{10.4230/LIPIcs.WADS.2025.45},
  annote =	{Keywords: Kd-tree, k-d tree, nearest neighbour search, Bregman divergence, decomposable Bregman divergence, KL divergence, relative entropy, cross entropy, Shannon’s entropy}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2016.3
Streaming Verification of Graph Properties

Authors: Amirali Abdullah, Samira Daruki, Chitradeep Dutta Roy, and Suresh Venkatasubramanian

Published in: LIPIcs, Volume 64, 27th International Symposium on Algorithms and Computation (ISAAC 2016)

Abstract
Streaming interactive proofs (SIPs) are a framework for outsourced computation. A computationally limited streaming client (the verifier) hands over a large data set to an untrusted server (the prover) in the cloud and the two parties run a protocol to confirm the correctness of result with high probability. SIPs are particularly interesting for problems that are hard to solve (or even approximate) well in a streaming setting. The most notable of these problems is finding maximum matchings, which has received intense interest in recent years but has strong lower bounds even for constant factor approximations. In this paper, we present efficient streaming interactive proofs that can verify maximum matchings exactly. Our results cover all flavors of matchings (bipartite/non-bipartite and weighted). In addition, we also present streaming verifiers for approximate metric TSP. In particular, these are the first efficient results for weighted matchings and for metric TSP in any streaming verification model.
Cite as

Amirali Abdullah, Samira Daruki, Chitradeep Dutta Roy, and Suresh Venkatasubramanian. Streaming Verification of Graph Properties. In 27th International Symposium on Algorithms and Computation (ISAAC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 64, pp. 3:1-3:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{abdullah_et_al:LIPIcs.ISAAC.2016.3,
  author =	{Abdullah, Amirali and Daruki, Samira and Roy, Chitradeep Dutta and Venkatasubramanian, Suresh},
  title =	{{Streaming Verification of Graph Properties}},
  booktitle =	{27th International Symposium on Algorithms and Computation (ISAAC 2016)},
  pages =	{3:1--3:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-026-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{64},
  editor =	{Hong, Seok-Hee},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2016.3},
  URN =		{urn:nbn:de:0030-drops-67730},
  doi =		{10.4230/LIPIcs.ISAAC.2016.3},
  annote =	{Keywords: streaming interactive proofs, verification, matching, travelling salesman problem, graph algorithms}
}
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