Published in: LIPIcs, Volume 302, 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)
Anna Brandenberger, Byron Chin, Nathan S. Sheffield, and Divya Shyamal. Matching Algorithms in the Sparse Stochastic Block Model. In 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 302, pp. 16:1-16:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{brandenberger_et_al:LIPIcs.AofA.2024.16, author = {Brandenberger, Anna and Chin, Byron and Sheffield, Nathan S. and Shyamal, Divya}, title = {{Matching Algorithms in the Sparse Stochastic Block Model}}, booktitle = {35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)}, pages = {16:1--16:21}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-329-4}, ISSN = {1868-8969}, year = {2024}, volume = {302}, editor = {Mailler, C\'{e}cile and Wild, Sebastian}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2024.16}, URN = {urn:nbn:de:0030-drops-204515}, doi = {10.4230/LIPIcs.AofA.2024.16}, annote = {Keywords: Matching Algorithms, Online Matching, Stochastic Block Model} }
Published in: LIPIcs, Volume 302, 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)
Sam Olesker-Taylor. Multicoloured Hardcore Model: Fast Mixing and Its Applications as a Scheduling Algorithm. In 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 302, pp. 20:1-20:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{oleskertaylor:LIPIcs.AofA.2024.20, author = {Olesker-Taylor, Sam}, title = {{Multicoloured Hardcore Model: Fast Mixing and Its Applications as a Scheduling Algorithm}}, booktitle = {35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)}, pages = {20:1--20:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-329-4}, ISSN = {1868-8969}, year = {2024}, volume = {302}, editor = {Mailler, C\'{e}cile and Wild, Sebastian}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2024.20}, URN = {urn:nbn:de:0030-drops-204558}, doi = {10.4230/LIPIcs.AofA.2024.20}, annote = {Keywords: mixing time, queueing theory, hardcore model, proper colourings, independent set, data transmission, randomised algorithms, routing, scheduling, multihop wireless networks} }
Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)
Yu Chen, Michael Kapralov, Mikhail Makarov, and Davide Mazzali. On the Streaming Complexity of Expander Decomposition. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 46:1-46:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{chen_et_al:LIPIcs.ICALP.2024.46, author = {Chen, Yu and Kapralov, Michael and Makarov, Mikhail and Mazzali, Davide}, title = {{On the Streaming Complexity of Expander Decomposition}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {46:1--46:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-322-5}, ISSN = {1868-8969}, year = {2024}, volume = {297}, editor = {Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.46}, URN = {urn:nbn:de:0030-drops-201890}, doi = {10.4230/LIPIcs.ICALP.2024.46}, annote = {Keywords: Graph Sketching, Dynamic Streaming, Expander Decomposition} }
Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)
Soheil Behnezhad, Mohammad Roghani, Aviad Rubinstein, and Amin Saberi. Sublinear Algorithms for TSP via Path Covers. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 19:1-19:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{behnezhad_et_al:LIPIcs.ICALP.2024.19, author = {Behnezhad, Soheil and Roghani, Mohammad and Rubinstein, Aviad and Saberi, Amin}, title = {{Sublinear Algorithms for TSP via Path Covers}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {19:1--19:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-322-5}, ISSN = {1868-8969}, year = {2024}, volume = {297}, editor = {Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.19}, URN = {urn:nbn:de:0030-drops-201623}, doi = {10.4230/LIPIcs.ICALP.2024.19}, annote = {Keywords: Sublinear Algorithms, Traveling Salesman Problem, Approximation Algorithm, (1, 2)-TSP, Graphic TSP} }
Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)
Charlie Carlson, Ewan Davies, Alexandra Kolla, and Aditya Potukuchi. A Spectral Approach to Approximately Counting Independent Sets in Dense Bipartite Graphs. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 35:1-35:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{carlson_et_al:LIPIcs.ICALP.2024.35, author = {Carlson, Charlie and Davies, Ewan and Kolla, Alexandra and Potukuchi, Aditya}, title = {{A Spectral Approach to Approximately Counting Independent Sets in Dense Bipartite Graphs}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {35:1--35:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-322-5}, ISSN = {1868-8969}, year = {2024}, volume = {297}, editor = {Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.35}, URN = {urn:nbn:de:0030-drops-201782}, doi = {10.4230/LIPIcs.ICALP.2024.35}, annote = {Keywords: approximate counting, independent sets, bipartite graphs, graph containers} }
Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)
Weiming Feng and Heng Guo. An FPRAS for Two Terminal Reliability in Directed Acyclic Graphs. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 62:1-62:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{feng_et_al:LIPIcs.ICALP.2024.62, author = {Feng, Weiming and Guo, Heng}, title = {{An FPRAS for Two Terminal Reliability in Directed Acyclic Graphs}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {62:1--62:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-322-5}, ISSN = {1868-8969}, year = {2024}, volume = {297}, editor = {Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.62}, URN = {urn:nbn:de:0030-drops-202057}, doi = {10.4230/LIPIcs.ICALP.2024.62}, annote = {Keywords: Approximate counting, Network reliability, Sampling algorithm} }
Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)
Yuda Feng and Shi Li. A Note on Approximating Weighted Nash Social Welfare with Additive Valuations. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 63:1-63:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{feng_et_al:LIPIcs.ICALP.2024.63, author = {Feng, Yuda and Li, Shi}, title = {{A Note on Approximating Weighted Nash Social Welfare with Additive Valuations}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {63:1--63:9}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-322-5}, ISSN = {1868-8969}, year = {2024}, volume = {297}, editor = {Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.63}, URN = {urn:nbn:de:0030-drops-202068}, doi = {10.4230/LIPIcs.ICALP.2024.63}, annote = {Keywords: Nash Social Welfare, Configuration LP, Approximation Algorithms} }
Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)
Yasushi Kawase, Koichi Nishimura, and Hanna Sumita. Minimizing Symmetric Convex Functions over Hybrid of Continuous and Discrete Convex Sets. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 96:1-96:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{kawase_et_al:LIPIcs.ICALP.2024.96, author = {Kawase, Yasushi and Nishimura, Koichi and Sumita, Hanna}, title = {{Minimizing Symmetric Convex Functions over Hybrid of Continuous and Discrete Convex Sets}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {96:1--96:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-322-5}, ISSN = {1868-8969}, year = {2024}, volume = {297}, editor = {Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.96}, URN = {urn:nbn:de:0030-drops-202393}, doi = {10.4230/LIPIcs.ICALP.2024.96}, annote = {Keywords: Integral base-polyhedron, Fair allocation, Matroid} }
Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)
Leonid Gurvits, Nathan Klein, and Jonathan Leake. From Trees to Polynomials and Back Again: New Capacity Bounds with Applications to TSP. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 79:1-79:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{gurvits_et_al:LIPIcs.ICALP.2024.79, author = {Gurvits, Leonid and Klein, Nathan and Leake, Jonathan}, title = {{From Trees to Polynomials and Back Again: New Capacity Bounds with Applications to TSP}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {79:1--79:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-322-5}, ISSN = {1868-8969}, year = {2024}, volume = {297}, editor = {Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.79}, URN = {urn:nbn:de:0030-drops-202229}, doi = {10.4230/LIPIcs.ICALP.2024.79}, annote = {Keywords: traveling salesman problem, strongly Rayleigh distributions, polynomial capacity, probability lower bounds, combinatorial lower bounds} }
Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)
Agastya Vibhuti Jha and Akash Kumar. A Sublinear Time Tester for Max-Cut on Clusterable Graphs. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 91:1-91:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
@InProceedings{jha_et_al:LIPIcs.ICALP.2024.91, author = {Jha, Agastya Vibhuti and Kumar, Akash}, title = {{A Sublinear Time Tester for Max-Cut on Clusterable Graphs}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {91:1--91:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-322-5}, ISSN = {1868-8969}, year = {2024}, volume = {297}, editor = {Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.91}, URN = {urn:nbn:de:0030-drops-202344}, doi = {10.4230/LIPIcs.ICALP.2024.91}, annote = {Keywords: Sublinear Algorithms, Graph Algorithms, Clusterable Graphs, Property Testung} }
Published in: LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)
Dorna Abdolazimi, Kasper Lindberg, and Shayan Oveis Gharan. On Optimization and Counting of Non-Broken Bases of Matroids. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 40:1-40:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
@InProceedings{abdolazimi_et_al:LIPIcs.APPROX/RANDOM.2023.40, author = {Abdolazimi, Dorna and Lindberg, Kasper and Gharan, Shayan Oveis}, title = {{On Optimization and Counting of Non-Broken Bases of Matroids}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)}, pages = {40:1--40:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-296-9}, ISSN = {1868-8969}, year = {2023}, volume = {275}, editor = {Megow, Nicole and Smith, Adam}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.40}, URN = {urn:nbn:de:0030-drops-188653}, doi = {10.4230/LIPIcs.APPROX/RANDOM.2023.40}, annote = {Keywords: Complexity, Hardness, Optimization, Counting, Random walk, Local to Global, Matroids} }
Published in: LIPIcs, Volume 264, 38th Computational Complexity Conference (CCC 2023)
Dorna Abdolazimi and Shayan Oveis Gharan. An Improved Trickle down Theorem for Partite Complexes. In 38th Computational Complexity Conference (CCC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 264, pp. 10:1-10:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
@InProceedings{abdolazimi_et_al:LIPIcs.CCC.2023.10, author = {Abdolazimi, Dorna and Oveis Gharan, Shayan}, title = {{An Improved Trickle down Theorem for Partite Complexes}}, booktitle = {38th Computational Complexity Conference (CCC 2023)}, pages = {10:1--10:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-282-2}, ISSN = {1868-8969}, year = {2023}, volume = {264}, editor = {Ta-Shma, Amnon}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2023.10}, URN = {urn:nbn:de:0030-drops-182807}, doi = {10.4230/LIPIcs.CCC.2023.10}, annote = {Keywords: Simplicial complexes, High dimensional expanders, Trickle down theorem, Bounded degree high dimensional expanders, Locally testable codes, Random walks} }
Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)
Anna R. Karlin. A (Slightly) Improved Approximation Algorithm for the Metric Traveling Salesperson Problem (Invited Talk). In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, p. 1:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
@InProceedings{karlin:LIPIcs.ICALP.2023.1, author = {Karlin, Anna R.}, title = {{A (Slightly) Improved Approximation Algorithm for the Metric Traveling Salesperson Problem}}, booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)}, pages = {1:1--1:1}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-278-5}, ISSN = {1868-8969}, year = {2023}, volume = {261}, editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.1}, URN = {urn:nbn:de:0030-drops-180531}, doi = {10.4230/LIPIcs.ICALP.2023.1}, annote = {Keywords: Traveling Salesperson Problem, approximation algorithm} }
Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)
Dorna Abdolazimi, Anna R. Karlin, Nathan Klein, and Shayan Oveis Gharan. Matroid Partition Property and the Secretary Problem. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 2:1-2:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
@InProceedings{abdolazimi_et_al:LIPIcs.ITCS.2023.2, author = {Abdolazimi, Dorna and Karlin, Anna R. and Klein, Nathan and Oveis Gharan, Shayan}, title = {{Matroid Partition Property and the Secretary Problem}}, booktitle = {14th Innovations in Theoretical Computer Science Conference (ITCS 2023)}, pages = {2:1--2:9}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-263-1}, ISSN = {1868-8969}, year = {2023}, volume = {251}, editor = {Tauman Kalai, Yael}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.2}, URN = {urn:nbn:de:0030-drops-175051}, doi = {10.4230/LIPIcs.ITCS.2023.2}, annote = {Keywords: Online algorithms, Matroids, Matroid secretary problem} }
Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)
Farzam Ebrahimnejad, Ansh Nagda, and Shayan Oveis Gharan. Counting and Sampling Perfect Matchings in Regular Expanding Non-Bipartite Graphs. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 61:1-61:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
@InProceedings{ebrahimnejad_et_al:LIPIcs.ITCS.2022.61, author = {Ebrahimnejad, Farzam and Nagda, Ansh and Gharan, Shayan Oveis}, title = {{Counting and Sampling Perfect Matchings in Regular Expanding Non-Bipartite Graphs}}, booktitle = {13th Innovations in Theoretical Computer Science Conference (ITCS 2022)}, pages = {61:1--61:12}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-217-4}, ISSN = {1868-8969}, year = {2022}, volume = {215}, editor = {Braverman, Mark}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.61}, URN = {urn:nbn:de:0030-drops-156579}, doi = {10.4230/LIPIcs.ITCS.2022.61}, annote = {Keywords: perfect matchings, approximate sampling, approximate counting, expanders} }