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Documents authored by Stubbs, Daniel M.


Found 2 Possible Name Variants:

Stubbs, Daniel M.

Document
Improved Streaming Algorithms for Weighted Matching, via Unweighted Matching

Authors: Michael Crouch and Daniel M. Stubbs

Published in: LIPIcs, Volume 28, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)


Abstract
We present a (4 + epsilon) approximation algorithm for weighted graph matching which applies in the semistreaming, sliding window, and MapReduce models; this single algorithm improves the previous best algorithm in each model. The algorithm operates by reducing the maximum-weight matching problem to a polylog number of copies of the maximum-cardinality matching problem. The algorithm also extends to provide approximation guarantees for the more general problem of finding weighted independent sets in p-systems (which include intersections of p matroids and p-bounded hypergraph matching).

Cite as

Michael Crouch and Daniel M. Stubbs. Improved Streaming Algorithms for Weighted Matching, via Unweighted Matching. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 28, pp. 96-104, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)


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@InProceedings{crouch_et_al:LIPIcs.APPROX-RANDOM.2014.96,
  author =	{Crouch, Michael and Stubbs, Daniel M.},
  title =	{{Improved Streaming Algorithms for Weighted Matching, via Unweighted Matching}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)},
  pages =	{96--104},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-74-3},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{28},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} and Devanur, Nikhil R. and Moore, Cristopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2014.96},
  URN =		{urn:nbn:de:0030-drops-46907},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2014.96},
  annote =	{Keywords: Streaming Algorithms, Graph Matching, Weighted Graph Matching, MapReduce, Independence Systems}
}

Stubbs, Daniel

Document
Metatheorems for Dynamic Weighted Matching

Authors: Daniel Stubbs and Virginia Vassilevska Williams

Published in: LIPIcs, Volume 67, 8th Innovations in Theoretical Computer Science Conference (ITCS 2017)


Abstract
We consider the maximum weight matching (MWM) problem in dynamic graphs. We provide two reductions. The first reduces the dynamic MWM problem on m-edge, n-node graphs with weights bounded by N to the problem with weights bounded by (n/eps)^2, so that if the MWM problem can be alpha-approximated with update time t(m,n,N), then it can also be (1+eps)alpha-approximated with update time O(t(m,n,(n/eps)^2)log^2 n+log n loglog N)). The second reduction reduces the dynamic MWM problem to the dynamic maximum cardinality matching (MCM) problem in which the graph is unweighted. This reduction shows that if there is an \alpha-approximation algorithm for MCM with update time t(m,n) in m-edge n-node graphs, then there is also a (2+eps)alpha-approximation algorithm for MWM with update time O(t(m,n)eps^{-2}log^2 N). We also obtain better bounds in our reductions if the ratio between the largest and the smallest edge weight is small. Combined with recent work on MCM, these two reductions substantially improve upon the state-of-the-art of dynamic MWM algorithms.

Cite as

Daniel Stubbs and Virginia Vassilevska Williams. Metatheorems for Dynamic Weighted Matching. In 8th Innovations in Theoretical Computer Science Conference (ITCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 67, pp. 58:1-58:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)


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@InProceedings{stubbs_et_al:LIPIcs.ITCS.2017.58,
  author =	{Stubbs, Daniel and Vassilevska Williams, Virginia},
  title =	{{Metatheorems for Dynamic Weighted Matching}},
  booktitle =	{8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
  pages =	{58:1--58:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-029-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{67},
  editor =	{Papadimitriou, Christos H.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2017.58},
  URN =		{urn:nbn:de:0030-drops-81944},
  doi =		{10.4230/LIPIcs.ITCS.2017.58},
  annote =	{Keywords: dynamic algorithms, maximum matching, maximum weight matching}
}
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