Abstract
We provide a simple algorithmic proof for the symmetric Lopsided Lovász Local Lemma, a variant of the classic Lovász Local Lemma, where, roughly, only the degree of the negatively correlated undesirable events counts. Our analysis refers to the algorithm by Moser (2009), however it is based on a simple application of the probabilistic method, rather than a counting argument, as are most of the analyses of algorithms for variants of the Lovász Local Lemma.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Erdős, P., Lovász, L.: Problems and results on 3-chromatic hypergraphs and some related questions. Infin. Finite Sets 10, 609–627 (1975)
Szegedy, M.: The Lovász local lemma – a survey. In: Bulatov, A.A., Shur, A.M. (eds.) CSR 2013. LNCS, vol. 7913, pp. 1–11. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38536-0_1
Moser, R.A.: A constructive proof of the Lovász local lemma. In: Proceedings of the 41st annual ACM Symposium on Theory of Computing, pp. 343–350 (2009)
Alon, N.: A parallel algorithmic version of the local lemma. Random Struct. Algorithms 2(4), 367–378 (1991)
Beck, J.: An algorithmic approach to the Lovász local lemma I. Random Struct. Algorithms 2(4), 343–365 (1991)
Srivinsan, A.: Improved algorithmic versions of the Lovász local lemma. In: Proceedings of the Nineteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 611–620. Society for Industrial and Applied Mathematics (2008)
Tao, T.: Moser’s entropy compression argument (2009). https://terrytao.wordpress.com/2009/08/05/mosers-entropy-compression-argument/
Spencer, J.: Robin Moser makes Lovász local lemma algorithmic! (2010). https://cs.nyu.edu/spencer/moserlovasz1.pdf
Giotis, I., Kirousis, L., Psaromiligkos, K.I., Thilikos, D.M.: On the algorithmic Lovász local lemma and acyclic edge coloring. In: Proceedings of the Twelfth Workshop on Analytic Algorithmics and Combinatorics. Society for Industrial and Applied Mathematics (2015). http://epubs.siam.org/doi/pdf/10.1137/1.9781611973761.2
Erdős, P., Spencer, J.: Lopsided Lovász local lemma and Latin transversals. Discret. Appl. Math. 30(2–3), 151–154 (1991)
Berman, P.R., Scott, A., Karpinski, M.: Approximation hardness and satisfiability of bounded occurrence instances of SAT. ECCC 10(022) (2003)
Gebauer, H., Moser, R.A., Scheder, D., Welzl, E.: The Lovász local lemma and satisfiability. Efficient Algorithms, pp. 30–54. Springer, Berlin (2009). https://doi.org/10.1007/978-3-642-03456-5_3
Gebauer, H., Szabó, T., Tardos, G.: The local lemma is tight for SAT. In: Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 664–674. SIAM (2011)
Moser, R.A., Tardos, G.: A constructive proof of the general Lovász local lemma. J. ACM (JACM) 57(2), 11 (2010)
Sarkar, K., Colbourn, C.J.: Upper bounds on the size of covering arrays. SIAM J. Discret. Math. 31(2), 1277–1293 (2017)
Kolipaka, K., Rao, B., Szegedy, M.: Moser and Tardos meet Lovász. In: Proceedings of the Forty-Third Annual ACM Symposium on Theory of Computing, pp. 235–244. ACM, New York (2011)
Shearer, J.B.: On a problem of Spencer. Combinatorica 5(3), 241–245 (1985)
Harvey, N.J.A., Vondrák, J.: An algorithmic proof of the Lovász local lemma via resampling oracles. In: Proceedings 56th Annual Symposium on Foundations of Computer Science (FOCS), pp. 1327–1346. IEEE (2015)
Harris, D.G.: Lopsidependency in the Moser-Tardos framework: beyond the lopsided Lovász local lemma. In: Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1792–1808. SIAM (2015)
Spencer, J.: Ten Lectures on the Probabilistic Method, vol. 64. SIAM, Philadelphia (1994)
Achlioptas, D., Iliopoulos, F.: Random walks that find perfect objects and the Lovász local lemma. In: 2014 IEEE 55th Annual Symposium on Foundations of Computer Science (FOCS), pp. 494–503. IEEE (2014)
Sedgewick, R., Flajolet, P.: An Introduction to the Analysis of Algorithms. Addison-Wesley, Upper Saddle River (2013)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Kirousis, L., Livieratos, J. (2019). A Simple Algorithmic Proof of the Symmetric Lopsided Lovász Local Lemma. In: Battiti, R., Brunato, M., Kotsireas, I., Pardalos, P. (eds) Learning and Intelligent Optimization. LION 12 2018. Lecture Notes in Computer Science(), vol 11353. Springer, Cham. https://doi.org/10.1007/978-3-030-05348-2_5
Download citation
DOI: https://doi.org/10.1007/978-3-030-05348-2_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-05347-5
Online ISBN: 978-3-030-05348-2
eBook Packages: Computer ScienceComputer Science (R0)