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Documents authored by Mirka, Renee

Document
Short Paper
DOI: 10.4230/LIPIcs.CP.2023.47
A New Approach to Finding 2 x n Partially Spatially Balanced Latin Rectangles (Short Paper)

Authors: Renee Mirka, Laura Greenstreet, Marc Grimson, and Carla P. Gomes

Published in: LIPIcs, Volume 280, 29th International Conference on Principles and Practice of Constraint Programming (CP 2023)

Abstract
Partially spatially balanced Latin rectangles are combinatorial structures that are important for experimental design. However, it is computationally challenging to find even small optimally balanced rectangles, where previous work has not been able to prove optimality for any rectangle with a dimension above size 11. Here we introduce a graph-based encoding for the 2 × n case based on finding the minimum-cost clique of size n. This encoding inspires a new mixed-integer programming (MIP) formulation, which finds exact solutions for the 2 × 12 and 2 × 13 cases and provides improved bounds up to n = 20. Compared to three other methods, the new formulation establishes the best lower bound in all cases and establishes the best upper bound in five out of seven cases.
Cite as

Renee Mirka, Laura Greenstreet, Marc Grimson, and Carla P. Gomes. A New Approach to Finding 2 x n Partially Spatially Balanced Latin Rectangles (Short Paper). In 29th International Conference on Principles and Practice of Constraint Programming (CP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 280, pp. 47:1-47:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{mirka_et_al:LIPIcs.CP.2023.47,
  author =	{Mirka, Renee and Greenstreet, Laura and Grimson, Marc and Gomes, Carla P.},
  title =	{{A New Approach to Finding 2 x n Partially Spatially Balanced Latin Rectangles}},
  booktitle =	{29th International Conference on Principles and Practice of Constraint Programming (CP 2023)},
  pages =	{47:1--47:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-300-3},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{280},
  editor =	{Yap, Roland H. C.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2023.47},
  URN =		{urn:nbn:de:0030-drops-190849},
  doi =		{10.4230/LIPIcs.CP.2023.47},
  annote =	{Keywords: Spatially balanced Latin squares, partially spatially balanced Latin rectangles, minimum edge weight clique, combinatorial optimization, mixed integer programming, imbalance, cliques}
}
Document
DOI: 10.4230/LIPIcs.SEA.2022.19
An Experimental Evaluation of Semidefinite Programming and Spectral Algorithms for Max Cut

Authors: Renee Mirka and David P. Williamson

Published in: LIPIcs, Volume 233, 20th International Symposium on Experimental Algorithms (SEA 2022)

Abstract
We experimentally evaluate the performance of several Max Cut approximation algorithms. In particular, we compare the results of the Goemans and Williamson algorithm using semidefinite programming with Trevisan’s algorithm using spectral partitioning. The former algorithm has a known .878 approximation guarantee whereas the latter has a .614 approximation guarantee. We investigate whether this gap in approximation guarantees is evident in practice or whether the spectral algorithm performs as well as the SDP. We also compare the performances to the standard greedy Max Cut algorithm which has a .5 approximation guarantee and two additional spectral algorithms. The algorithms are tested on Erdős-Renyi random graphs, complete graphs from TSPLIB, and real-world graphs from the Network Repository. We find, unsurprisingly, that the spectral algorithms provide a significant speed advantage over the SDP. In our experiments, the spectral algorithms return cuts with values which are competitive with those of the SDP.
Cite as

Renee Mirka and David P. Williamson. An Experimental Evaluation of Semidefinite Programming and Spectral Algorithms for Max Cut. In 20th International Symposium on Experimental Algorithms (SEA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 233, pp. 19:1-19:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{mirka_et_al:LIPIcs.SEA.2022.19,
  author =	{Mirka, Renee and Williamson, David P.},
  title =	{{An Experimental Evaluation of Semidefinite Programming and Spectral Algorithms for Max Cut}},
  booktitle =	{20th International Symposium on Experimental Algorithms (SEA 2022)},
  pages =	{19:1--19:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-251-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{233},
  editor =	{Schulz, Christian and U\c{c}ar, Bora},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2022.19},
  URN =		{urn:nbn:de:0030-drops-165533},
  doi =		{10.4230/LIPIcs.SEA.2022.19},
  annote =	{Keywords: Max Cut, Approximation Algorithms}
}
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