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Documents authored by Goldberg, Andrew V.

Document
DOI: 10.4230/LIPIcs.ESA.2022.45
A Local Search Algorithm for Large Maximum Weight Independent Set Problems

Authors: Yuanyuan Dong, Andrew V. Goldberg, Alexander Noe, Nikos Parotsidis, Mauricio G.C. Resende, and Quico Spaen

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

Abstract
Motivated by a real-world vehicle routing application, we consider the maximum-weight independent set problem: Given a node-weighted graph, find a set of independent (mutually nonadjacent) nodes whose node-weight sum is maximum. Some of the graphs arising in the vehicle routing application are large, having hundreds of thousands of nodes and hundreds of millions of edges. To solve instances of this size, we develop a new local search algorithm, which is a metaheuristic based on the greedy randomized adaptive search (GRASP) framework. This algorithm, named METAMIS, uses a wider range of simple local search operations than previously described in the literature. We introduce data structures that make these operations efficient. A new variant of path-relinking is introduced to escape local optima and so is a new alternating augmenting-path local search move that improves algorithm performance. We compare an implementation of our algorithm with a state-of-the-art publicly available code on public benchmark sets, including some large instances. Our algorithm is, in general, competitive and outperforms this openly available code on large vehicle routing instances of the maximum weight independent set problem. We hope that our results will lead to even better maximum-weight independent set algorithms.
Cite as

Yuanyuan Dong, Andrew V. Goldberg, Alexander Noe, Nikos Parotsidis, Mauricio G.C. Resende, and Quico Spaen. A Local Search Algorithm for Large Maximum Weight Independent Set Problems. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 45:1-45:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{dong_et_al:LIPIcs.ESA.2022.45,
  author =	{Dong, Yuanyuan and Goldberg, Andrew V. and Noe, Alexander and Parotsidis, Nikos and Resende, Mauricio G.C. and Spaen, Quico},
  title =	{{A Local Search Algorithm for Large Maximum Weight Independent Set Problems}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{45:1--45:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.45},
  URN =		{urn:nbn:de:0030-drops-169839},
  doi =		{10.4230/LIPIcs.ESA.2022.45},
  annote =	{Keywords: GRASP, local search, maximum-weight independent set, path-relinking, heuristic, metaheuristic}
}
Document
DOI: 10.4230/LIPIcs.STACS.2015.406
Minimum Cost Flows in Graphs with Unit Capacities

Authors: Andrew V. Goldberg, Haim Kaplan, Sagi Hed, and Robert E. Tarjan

Published in: LIPIcs, Volume 30, 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)

Abstract
We consider the minimum cost flow problem on graphs with unit capacities and its special cases. In previous studies, special purpose algorithms exploiting the fact that capacities are one have been developed. In contrast, for maximum flow with unit capacities, the best bounds are proven for slight modifications of classical blocking flow and push-relabel algorithms. In this paper we show that the classical cost scaling algorithms of Goldberg and Tarjan (for general integer capacities) applied to a problem with unit capacities achieve or improve the best known bounds. For weighted bipartite matching we establish a bound of O(\sqrt{rm}\log C) on a slight variation of this algorithm. Here r is the size of the smaller side of the bipartite graph, m is the number of edges, and C is the largest absolute value of an arc-cost. This simplifies a result of [Duan et al. 2011] and improves the bound, answering an open question of [Tarjan and Ramshaw 2012]. For graphs with unit vertex capacities we establish a novel O(\sqrt{n}m\log(nC)) bound. We also give the first cycle canceling algorithm for minimum cost flow with unit capacities. The algorithm naturally generalizes the single source shortest path algorithm of [Goldberg 1995].
Cite as

Andrew V. Goldberg, Haim Kaplan, Sagi Hed, and Robert E. Tarjan. Minimum Cost Flows in Graphs with Unit Capacities. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 406-419, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{goldberg_et_al:LIPIcs.STACS.2015.406,
  author =	{Goldberg, Andrew V. and Kaplan, Haim and Hed, Sagi and Tarjan, Robert E.},
  title =	{{Minimum Cost Flows in Graphs with Unit Capacities}},
  booktitle =	{32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
  pages =	{406--419},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-78-1},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{30},
  editor =	{Mayr, Ernst W. and Ollinger, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.406},
  URN =		{urn:nbn:de:0030-drops-49304},
  doi =		{10.4230/LIPIcs.STACS.2015.406},
  annote =	{Keywords: minimum cost flow, bipartite matching, unit capacity, cost scaling}
}
Document
DOI: 10.4230/DagRep.3.9.169
Algorithm Engineering (Dagstuhl Seminar 13391)

Authors: Andrew V. Goldberg, Giuseppe F. Italiano, David S. Johnson, and Dorothea Wagner

Published in: Dagstuhl Reports, Volume 3, Issue 9 (2014)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 13391 "Algorithm Engineering". The algorithm engineering approach consists of a cycle of algorithm design, analysis, implementation, and experimental evaluation, with the aim of bridging the gap between theory and practice in the area of algorithms. This cycle of phases is driven by falsifiable hypotheses validated by experiments. Moreover, real-world instances often have direct impact on this cycle since they often expose modeling and analysis shortcomings. Algorithm engineering touches other research areas such as algorithm theory, combinatorial optimization, computer architecture, parallel and distributed computing, high-performance computing, and operations research. Prominent success stories in algorithm engineering include the linear program solver CPLEX, the traveling salesman suite CONCORDE, speed-up techniques for shortest paths computation, for example, in route planning, as well as graph partitioning and the computation of Steiner trees. All these topics are driven by the need for efficient algorithms and libraries for problems that appear frequently in real-world applications. In the last fifteen years, this approach to algorithmic research has gained increasing attention. There is an ACM Journal on Experimental Algorithmics and several annual conferences (WAE/ESA applied track since 1997, Alenex since 1998, and WEA/SEA since 2001) and the series of DIMACS implementation challenges where people meet to compare implementations for a specific problem. From 2007 to 2013 the German Research Foundation also funded a special priority program on algorithm engineering (DFG SPP 1307).
Cite as

Andrew V. Goldberg, Giuseppe F. Italiano, David S. Johnson, and Dorothea Wagner. Algorithm Engineering (Dagstuhl Seminar 13391). In Dagstuhl Reports, Volume 3, Issue 9, pp. 169-189, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@Article{goldberg_et_al:DagRep.3.9.169,
  author =	{Goldberg, Andrew V. and Italiano, Giuseppe F. and Johnson, David S. and Wagner, Dorothea},
  title =	{{Algorithm Engineering (Dagstuhl Seminar 13391)}},
  pages =	{169--189},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2014},
  volume =	{3},
  number =	{9},
  editor =	{Goldberg, Andrew V. and Italiano, Giuseppe F. and Johnson, David S. and Wagner, Dorothea},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.3.9.169},
  URN =		{urn:nbn:de:0030-drops-44214},
  doi =		{10.4230/DagRep.3.9.169},
  annote =	{Keywords: Algorithm Engineering, Science of Algorithmics, Manycore Algorithms, Certifying Algorithms, Web Search, Large Graphs}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2011.52
Faster Batched Shortest Paths in Road Networks

Authors: Daniel Delling, Andrew V. Goldberg, and Renato F. Werneck

Published in: OASIcs, Volume 20, 11th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (2011)

Abstract
We study the problem of computing batched shortest paths in road networks efficiently. Our focus is on computing paths from a single source to multiple targets (one-to-many queries). We perform a comprehensive experimental comparison of several approaches, including new ones. We conclude that a new extension of PHAST (a recent one-to-all algorithm), called RPHAST, has the best performance in most cases, often by orders of magnitude. When used to compute distance tables (many-to-many queries), RPHAST often outperforms all previous approaches.
Cite as

Daniel Delling, Andrew V. Goldberg, and Renato F. Werneck. Faster Batched Shortest Paths in Road Networks. In 11th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems. Open Access Series in Informatics (OASIcs), Volume 20, pp. 52-63, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{delling_et_al:OASIcs.ATMOS.2011.52,
  author =	{Delling, Daniel and Goldberg, Andrew V. and Werneck, Renato F.},
  title =	{{Faster Batched Shortest Paths in Road Networks}},
  booktitle =	{11th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems},
  pages =	{52--63},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-33-0},
  ISSN =	{2190-6807},
  year =	{2011},
  volume =	{20},
  editor =	{Caprara, Alberto and Kontogiannis, Spyros},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2011.52},
  URN =		{urn:nbn:de:0030-drops-32663},
  doi =		{10.4230/OASIcs.ATMOS.2011.52},
  annote =	{Keywords: shortest paths, contraction hierarchies, many-to-many, one-to-many}
}
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