4 Search Results for "Mehrabi, Ali D."

Document
DOI: 10.4230/LIPIcs.SoCG.2025.42
Range Counting Oracles for Geometric Problems

Authors: Anne Driemel, Morteza Monemizadeh, Eunjin Oh, Frank Staals, and David P. Woodruff

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
In this paper, we study estimators for geometric optimization problems in the sublinear geometric model. In this model, we have oracle access to a point set with size n in a discrete space [Δ]^d, where queries can be made to an oracle that responds to orthogonal range counting requests. The query complexity of an optimization problem is measured by the number of oracle queries required to compute an estimator for the problem. We investigate two problems in this framework, the Euclidean Minimum Spanning Tree (MST) and Earth Mover Distance (EMD). For EMD, we show the existence of an estimator that approximates the cost of EMD with O(log Δ)-relative error and O(nΔ/(s^{1+1/d}))-additive error using O(s polylog Δ) range counting queries for any parameter s with 1 ≤ s ≤ n. Moreover, we prove that this bound is tight. For MST, we demonstrate that the weight of MST can be estimated within a factor of (1 ± ε) using Õ(√n) range counting queries.
Cite as

Anne Driemel, Morteza Monemizadeh, Eunjin Oh, Frank Staals, and David P. Woodruff. Range Counting Oracles for Geometric Problems. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 42:1-42:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{driemel_et_al:LIPIcs.SoCG.2025.42,
  author =	{Driemel, Anne and Monemizadeh, Morteza and Oh, Eunjin and Staals, Frank and Woodruff, David P.},
  title =	{{Range Counting Oracles for Geometric Problems}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{42:1--42:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.42},
  URN =		{urn:nbn:de:0030-drops-231941},
  doi =		{10.4230/LIPIcs.SoCG.2025.42},
  annote =	{Keywords: Range counting oracles, minimum spanning trees, Earth Mover’s Distance}
}
Document
Position
DOI: 10.4230/TGDK.1.1.2
Large Language Models and Knowledge Graphs: Opportunities and Challenges

Authors: Jeff Z. Pan, Simon Razniewski, Jan-Christoph Kalo, Sneha Singhania, Jiaoyan Chen, Stefan Dietze, Hajira Jabeen, Janna Omeliyanenko, Wen Zhang, Matteo Lissandrini, Russa Biswas, Gerard de Melo, Angela Bonifati, Edlira Vakaj, Mauro Dragoni, and Damien Graux

Published in: TGDK, Volume 1, Issue 1 (2023): Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge, Volume 1, Issue 1

Abstract
Large Language Models (LLMs) have taken Knowledge Representation - and the world - by storm. This inflection point marks a shift from explicit knowledge representation to a renewed focus on the hybrid representation of both explicit knowledge and parametric knowledge. In this position paper, we will discuss some of the common debate points within the community on LLMs (parametric knowledge) and Knowledge Graphs (explicit knowledge) and speculate on opportunities and visions that the renewed focus brings, as well as related research topics and challenges.
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Jeff Z. Pan, Simon Razniewski, Jan-Christoph Kalo, Sneha Singhania, Jiaoyan Chen, Stefan Dietze, Hajira Jabeen, Janna Omeliyanenko, Wen Zhang, Matteo Lissandrini, Russa Biswas, Gerard de Melo, Angela Bonifati, Edlira Vakaj, Mauro Dragoni, and Damien Graux. Large Language Models and Knowledge Graphs: Opportunities and Challenges. In Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge (TGDK), Volume 1, Issue 1, pp. 2:1-2:38, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Article{pan_et_al:TGDK.1.1.2,
  author =	{Pan, Jeff Z. and Razniewski, Simon and Kalo, Jan-Christoph and Singhania, Sneha and Chen, Jiaoyan and Dietze, Stefan and Jabeen, Hajira and Omeliyanenko, Janna and Zhang, Wen and Lissandrini, Matteo and Biswas, Russa and de Melo, Gerard and Bonifati, Angela and Vakaj, Edlira and Dragoni, Mauro and Graux, Damien},
  title =	{{Large Language Models and Knowledge Graphs: Opportunities and Challenges}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{2:1--2:38},
  year =	{2023},
  volume =	{1},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.1.1.2},
  URN =		{urn:nbn:de:0030-drops-194766},
  doi =		{10.4230/TGDK.1.1.2},
  annote =	{Keywords: Large Language Models, Pre-trained Language Models, Knowledge Graphs, Ontology, Retrieval Augmented Language Models}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2017.4
Minimum Perimeter-Sum Partitions in the Plane

Authors: Mikkel Abrahamsen, Mark de Berg, Kevin Buchin, Mehran Mehr, and Ali D. Mehrabi

Published in: LIPIcs, Volume 77, 33rd International Symposium on Computational Geometry (SoCG 2017)

Abstract
Let P be a set of n points in the plane. We consider the problem of partitioning P into two subsets P_1 and P_2 such that the sum of the perimeters of CH(P_1) and CH(P_2) is minimized, where CH(P_i) denotes the convex hull of P_i. The problem was first studied by Mitchell and Wynters in 1991 who gave an O(n^2) time algorithm. Despite considerable progress on related problems, no subquadratic time algorithm for this problem was found so far. We present an exact algorithm solving the problem in O(n log^4 n) time and a (1+e)-approximation algorithm running in O(n + 1/e^2 log^4(1/e)) time.
Cite as

Mikkel Abrahamsen, Mark de Berg, Kevin Buchin, Mehran Mehr, and Ali D. Mehrabi. Minimum Perimeter-Sum Partitions in the Plane. In 33rd International Symposium on Computational Geometry (SoCG 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 77, pp. 4:1-4:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{abrahamsen_et_al:LIPIcs.SoCG.2017.4,
  author =	{Abrahamsen, Mikkel and de Berg, Mark and Buchin, Kevin and Mehr, Mehran and Mehrabi, Ali D.},
  title =	{{Minimum Perimeter-Sum Partitions in the Plane}},
  booktitle =	{33rd International Symposium on Computational Geometry (SoCG 2017)},
  pages =	{4:1--4:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-038-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{77},
  editor =	{Aronov, Boris and Katz, Matthew J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2017.4},
  URN =		{urn:nbn:de:0030-drops-72048},
  doi =		{10.4230/LIPIcs.SoCG.2017.4},
  annote =	{Keywords: Computational geometry, clustering, minimum-perimeter partition, convex hull}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2017.5
Range-Clustering Queries

Authors: Mikkel Abrahamsen, Mark de Berg, Kevin Buchin, Mehran Mehr, and Ali D. Mehrabi

Published in: LIPIcs, Volume 77, 33rd International Symposium on Computational Geometry (SoCG 2017)

Abstract
In a geometric k-clustering problem the goal is to partition a set of points in R^d into k subsets such that a certain cost function of the clustering is minimized. We present data structures for orthogonal range-clustering queries on a point set S: given a query box Q and an integer k > 2, compute an optimal k-clustering for the subset of S inside Q. We obtain the following results. * We present a general method to compute a (1+epsilon)-approximation to a range-clustering query, where epsilon>0 is a parameter that can be specified as part of the query. Our method applies to a large class of clustering problems, including k-center clustering in any Lp-metric and a variant of k-center clustering where the goal is to minimize the sum (instead of maximum) of the cluster sizes. * We extend our method to deal with capacitated k-clustering problems, where each of the clusters should not contain more than a given number of points. * For the special cases of rectilinear k-center clustering in R^1, and in R^2 for k = 2 or 3, we present data structures that answer range-clustering queries exactly.
Cite as

Mikkel Abrahamsen, Mark de Berg, Kevin Buchin, Mehran Mehr, and Ali D. Mehrabi. Range-Clustering Queries. In 33rd International Symposium on Computational Geometry (SoCG 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 77, pp. 5:1-5:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{abrahamsen_et_al:LIPIcs.SoCG.2017.5,
  author =	{Abrahamsen, Mikkel and de Berg, Mark and Buchin, Kevin and Mehr, Mehran and Mehrabi, Ali D.},
  title =	{{Range-Clustering Queries}},
  booktitle =	{33rd International Symposium on Computational Geometry (SoCG 2017)},
  pages =	{5:1--5:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-038-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{77},
  editor =	{Aronov, Boris and Katz, Matthew J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2017.5},
  URN =		{urn:nbn:de:0030-drops-72147},
  doi =		{10.4230/LIPIcs.SoCG.2017.5},
  annote =	{Keywords: Geometric data structures, clustering, k-center problem}
}
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