5 Search Results for "Mirka, Renee"

Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.27
Triangles Improve 0.878 Approximation for Maxcut

Authors: Fredie George, Anand Louis, and Rameesh Paul

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
Maxcut is a fundamental problem in graph algorithms, extensively studied for its theoretical and practical significance. The goal is to partition the vertex set of a graph G = (V, E) into disjoint subsets S and V⧵S so as to maximize the number of edges crossing the cut (S,V⧵S). The seminal work of Goemans and Williamson [Goemans and Williamson, 1995] introduced a semidefinite programming (SDP) based algorithm achieving a α_{GW} ≈ 0.87856-approximation for general graphs, guaranteed to be optimal under the Unique Games Conjecture [Khot, 2002; Khot et al., 2007]. We revisit the Goemans–Williamson SDP and prove that the standard Maxcut SDP achieves a (α_{GW} + Ω(1))-approximation whenever the input graph contains Ω(|E|) edge-disjoint triangles. Our analysis builds on classical rounding techniques studied in [Goemans and Williamson, 1995; Zwick, 1999] and introduces a refined understanding of the SDP solution structure in regimes where the previous guarantees are tight. Our result identifies a simple combinatorial property that may be satisfied by many natural graph classes. As applications, we show that unit ball graphs and graphs satisfying a spectral transitivity condition (as studied in [Gupta et al., 2016; Basu et al., 2024]) meet our structural criterion, and therefore we get better than α_{GW} approximation guarantees for them. Our algorithm runs in nearly linear time 𝒪̃(|E|), offering a more practical alternative to the PTAS of [Jansen et al., 2005] for unit ball graphs, which has exponential dependence on the approximation parameter.
Cite as

Fredie George, Anand Louis, and Rameesh Paul. Triangles Improve 0.878 Approximation for Maxcut. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 27:1-27:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{george_et_al:LIPIcs.APPROX/RANDOM.2025.27,
  author =	{George, Fredie and Louis, Anand and Paul, Rameesh},
  title =	{{Triangles Improve 0.878 Approximation for Maxcut}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{27:1--27:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.27},
  URN =		{urn:nbn:de:0030-drops-243931},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.27},
  annote =	{Keywords: Approximation Algorithms, Maxcut, Semidefinite Programming, Edge-disjoint Triangles, Unit Ball Graphs, Spectral Triadic Graphs}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.28
Approximation Algorithms for the Generalized Point-To-Point Problem

Authors: Zachary Friggstad, Mohammad R. Salavatipour, and Hao Sun

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
We consider the Generalized Point-to-Point (GP2P) problem in which we have an edge-weighted graph G with (possibly negative) node charges ϕ(v) ∈ ℤ. The goal is to find a minimum-cost set of edges such that each component has nonnegative total charge. Viewing the positive charges as specifying supply and negative charges as demand quantities at various nodes, the problem is equivalent to build the cheapest network so that it is possible to satisfy all demands by routing supplies across the network. This problem is a significant generalization of other network design problems such as the well-studied Steiner Forest problem. Even the special case of only having one single demand point (having charge -k and all the other nodes having charge +1) is capturing the k-Minimum Spanning Tree problem. Earlier work by Hajiaghayi et al. (2016) [Hajiaghayi et al., 2016] gave an O(log n) approximation in pseudo-polynomial time with further improved guarantees if the total supply is not much larger than the total demand, and also a 2-approximation if the total supply equals the total demand. Our contributions are four-fold: (a) we show how known k-Minimum Spanning Tree approximations can be extended to GP2P approximations while losing only a ε-factor if the number of demand points in the instance is bounded by a constant, (b) we improve the running time to be Fixed-Parameter Tractable (FPT) in the number of demand points in constant-dimensional Euclidean metrics, (c) we give a 2-approximation in instances where edge costs are all 1 and ϕ(v) = ± 1 for each node v and show such instances are APX-hard, and (d) we show how the logarithmic approximations in earlier work can be modified to run in truly polynomial time.
Cite as

Zachary Friggstad, Mohammad R. Salavatipour, and Hao Sun. Approximation Algorithms for the Generalized Point-To-Point Problem. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 28:1-28:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{friggstad_et_al:LIPIcs.WADS.2025.28,
  author =	{Friggstad, Zachary and Salavatipour, Mohammad R. and Sun, Hao},
  title =	{{Approximation Algorithms for the Generalized Point-To-Point Problem}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{28:1--28:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.28},
  URN =		{urn:nbn:de:0030-drops-242599},
  doi =		{10.4230/LIPIcs.WADS.2025.28},
  annote =	{Keywords: Point-to-Point Network design, Approximation, Steiner Forest, k-MST}
}
Document
DOI: 10.4230/LIPIcs.CP.2025.36
Balancing Latin Rectangles with LLM-Generated Streamliners

Authors: Florentina Voboril, Vaidyanathan Peruvemba Ramaswamy, and Stefan Szeider

Published in: LIPIcs, Volume 340, 31st International Conference on Principles and Practice of Constraint Programming (CP 2025)

Abstract
We present an integration of Large Language Models (LLMs) with streamlining techniques to find well-balanced Latin rectangles. Our approach combines LLM-generated streamlining constraints that effectively partition the search space, directing constraint solvers toward structured subspaces containing high-quality solutions. Our methodology extends LLM-generated streamliners, as Voboril et al. (2024) introduced for decision problems, to the optimization context through techniques that incrementally refine the objective function value. We propose two complementary strategies to orchestrate sets of streamliners: an incremental mechanism that utilizes improving solutions to initialize subsequent search processes, and an evolutionary framework that maintains and refines effective streamliner populations. Our experiments demonstrate that our approach successfully reduces established minimum imbalance values for partially spatially balanced Latin rectangles across multiple problem dimensions. The results validate the efficacy of combining LLMs with constraint programming methodologies for tackling problems characterized by complex global constraints.
Cite as

Florentina Voboril, Vaidyanathan Peruvemba Ramaswamy, and Stefan Szeider. Balancing Latin Rectangles with LLM-Generated Streamliners. In 31st International Conference on Principles and Practice of Constraint Programming (CP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 340, pp. 36:1-36:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{voboril_et_al:LIPIcs.CP.2025.36,
  author =	{Voboril, Florentina and Peruvemba Ramaswamy, Vaidyanathan and Szeider, Stefan},
  title =	{{Balancing Latin Rectangles with LLM-Generated Streamliners}},
  booktitle =	{31st International Conference on Principles and Practice of Constraint Programming (CP 2025)},
  pages =	{36:1--36:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-380-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{340},
  editor =	{de la Banda, Maria Garcia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2025.36},
  URN =		{urn:nbn:de:0030-drops-238970},
  doi =		{10.4230/LIPIcs.CP.2025.36},
  annote =	{Keywords: Balanced Latin Rectangles, Streamliners, Large Language Models, Warmstarts, Evolutionary Search}
}
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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