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Documents authored by Pothen, Alex

Document
DOI: 10.4230/DagRep.14.5.12
Discrete Algorithms on Modern and Emerging Compute Infrastructure (Dagstuhl Seminar 24201)

Authors: Kathrin Hanauer, Uwe Naumann, Alex Pothen, and Robert Schreiber

Published in: Dagstuhl Reports, Volume 14, Issue 5 (2024)

Abstract
Inspired by three plenary talks by leading figures in the area of "Discrete algorithms on modern and emerging compute infrastructure" this Dagstuhl Seminar emphasized focus sessions and working groups to dive into this very versatile topic. Lively discussions between experts from academia, research laboratories, and industry yielded a number of promising prospects for follow-up activities. As always, Dagstuhl provided the perfect setting for this kind of scientific exchange.
Cite as

Kathrin Hanauer, Uwe Naumann, Alex Pothen, and Robert Schreiber. Discrete Algorithms on Modern and Emerging Compute Infrastructure (Dagstuhl Seminar 24201). In Dagstuhl Reports, Volume 14, Issue 5, pp. 12-24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{hanauer_et_al:DagRep.14.5.12,
  author =	{Hanauer, Kathrin and Naumann, Uwe and Pothen, Alex and Schreiber, Robert},
  title =	{{Discrete Algorithms on Modern and Emerging Compute Infrastructure (Dagstuhl Seminar 24201)}},
  pages =	{12--24},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2024},
  volume =	{14},
  number =	{5},
  editor =	{Hanauer, Kathrin and Naumann, Uwe and Pothen, Alex and Schreiber, Robert},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.14.5.12},
  URN =		{urn:nbn:de:0030-drops-222672},
  doi =		{10.4230/DagRep.14.5.12},
  annote =	{Keywords: Combinatorial Scientific Computing, Discrete Algorithms, Graph Algorithms, High-Performance Computing}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.53
Semi-Streaming Algorithms for Weighted k-Disjoint Matchings

Authors: S M Ferdous, Bhargav Samineni, Alex Pothen, Mahantesh Halappanavar, and Bala Krishnamoorthy

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
We design and implement two single-pass semi-streaming algorithms for the maximum weight k-disjoint matching (k-DM) problem. Given an integer k, the k-DM problem is to find k pairwise edge-disjoint matchings such that the sum of the weights of the matchings is maximized. For k ≥ 2, this problem is NP-hard. Our first algorithm is based on the primal-dual framework of a linear programming relaxation of the problem and is 1/(3+ε)-approximate. We also develop an approximation preserving reduction from k-DM to the maximum weight b-matching problem. Leveraging this reduction and an existing semi-streaming b-matching algorithm, we design a (1/(2+ε))(1 - 1/(k+1))-approximate semi-streaming algorithm for k-DM. For any constant ε > 0, both of these algorithms require O(nk log_{1+ε}² n) bits of space. To the best of our knowledge, this is the first study of semi-streaming algorithms for the k-DM problem. We compare our two algorithms to state-of-the-art offline algorithms on 95 real-world and synthetic test problems, including thirteen graphs generated from data center network traces. On these instances, our streaming algorithms used significantly less memory (ranging from 6× to 512× less) and were faster in runtime than the offline algorithms. Our solutions were often within 5% of the best weights from the offline algorithms. We highlight that the existing offline algorithms run out of 1 TB memory for most of the large instances (> 1 billion edges), whereas our streaming algorithms can solve these problems using only 100 GB memory for k = 8.
Cite as

S M Ferdous, Bhargav Samineni, Alex Pothen, Mahantesh Halappanavar, and Bala Krishnamoorthy. Semi-Streaming Algorithms for Weighted k-Disjoint Matchings. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 53:1-53:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ferdous_et_al:LIPIcs.ESA.2024.53,
  author =	{Ferdous, S M and Samineni, Bhargav and Pothen, Alex and Halappanavar, Mahantesh and Krishnamoorthy, Bala},
  title =	{{Semi-Streaming Algorithms for Weighted k-Disjoint Matchings}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{53:1--53:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.53},
  URN =		{urn:nbn:de:0030-drops-211245},
  doi =		{10.4230/LIPIcs.ESA.2024.53},
  annote =	{Keywords: Matchings, Semi-Streaming Algorithms, Approximation Algorithms}
}
Document
DOI: 10.4230/LIPIcs.SEA.2024.12
Streaming Matching and Edge Cover in Practice

Authors: S M Ferdous, Alex Pothen, and Mahantesh Halappanavar

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract
Graph algorithms with polynomial space and time requirements often become infeasible for massive graphs with billions of edges or more. State-of-the-art approaches therefore employ approximate serial, parallel, and distributed algorithms to tackle these challenges. However, such approaches require storing the entire graph in memory and thus need access to costly computing resources such as clusters and supercomputers. In this paper, we present practical streaming approaches for solving massive graph problems using limited memory for two prototypical graph problems: maximum weighted matching and minimum weighted edge cover. For matching, we conduct a thorough computational study on two of the semi-streaming algorithms including a recent breakthrough result that achieves a 1/(2+ε)-approximation of the weight while using O(n log W /ε) memory (here n is the number of vertices and W is the maximum edge weight), designed by Paz and Schwartzman [SODA, 2017]. Empirically, we show that the semi-streaming algorithms produce matchings whose weight is close to the best 1/2-approximate offline algorithm while requiring less time and an order-of-magnitude less memory. For minimum weighted edge cover, we develop three novel semi-streaming algorithms. Two of these algorithms require a single pass through the input graph, require O(n log n) memory, and provide a 2-approximation guarantee on the objective. We also leverage a relationship between approximate maximum weighted matching and approximate minimum weighted edge cover to develop a two-pass 3/2+ε-approximate algorithm with the memory requirement of Paz and Schwartzman’s semi-streaming matching algorithm. These streaming approaches are compared against the state-of-the-art 3/2-approximate offline algorithm. The semi-streaming matching and the novel edge cover algorithms proposed in this paper can process graphs with several billions of edges in under 30 minutes using 6 GB of memory, which is at least an order of magnitude improvement from the offline (non-streaming) algorithms. For the largest graph, the best alternative offline parallel approximation algorithm (GPA+ROMA) could not finish in three hours even while employing hundreds of processors and 1 TB of memory. We also demonstrate an application of semi-streaming algorithm by computing a matching using linearly bounded memory on intersection graphs derived from three machine learning datasets, while the existing offline algorithms could not complete on one of these datasets since its memory requirement exceeded 1TB.
Cite as

S M Ferdous, Alex Pothen, and Mahantesh Halappanavar. Streaming Matching and Edge Cover in Practice. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 12:1-12:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ferdous_et_al:LIPIcs.SEA.2024.12,
  author =	{Ferdous, S M and Pothen, Alex and Halappanavar, Mahantesh},
  title =	{{Streaming Matching and Edge Cover in Practice}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{12:1--12:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.12},
  URN =		{urn:nbn:de:0030-drops-203773},
  doi =		{10.4230/LIPIcs.SEA.2024.12},
  annote =	{Keywords: Matching, Edge Cover, Semi-Streaming Algorithm, Parallel Algorithms, Algorithm Engineering}
}
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