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The Combinatorial Santa Claus Problem or: How to Find Good Matchings in Non-Uniform Hypergraphs [article]

Etienne Bamas, Paritosh Garg, Lars Rohwedder
2020 arXiv   pre-print
We dub this problem the Combinatorial Santa Claus problem, since we show in this paper that this problem and the Santa Claus problem are almost equivalent in terms of their approximability.  ...  The non-trivial observation that any uniform regular hypergraph admits a relaxed matching for α = O(1) was a major step in obtaining a constant approximation rate for a special case of the Santa Claus  ...  On the connection to the Santa Claus problem In this section, we show how the Santa Claus problem and the Combinatorial Santa Claus problem are almost equivalent in terms of approximability.  ... 
arXiv:2007.09116v2 fatcat:fz45a4smiza5fbqfh3jg3c2eh4

The Submodular Santa Claus Problem in the Restricted Assignment Case [article]

Etienne Bamas, Paritosh Garg, Lars Rohwedder
2020 arXiv   pre-print
The submodular Santa Claus problem was introduced in a seminal work by Goemans, Harvey, Iwata, and Mirrokni (SODA'09) as an application of their structural result.  ...  In the mentioned problem n unsplittable resources have to be assigned to m players, each with a monotone submodular utility function f_i. The goal is to maximize min_i f_i(S_i) where S_1,...  ...  Additional implications of non-uniform hypergraph matchings to the Santa Claus problem. We believe this hypergraph matching problem is interesting in its own right.  ... 
arXiv:2011.06939v1 fatcat:qh4ysuy2ufcg3cwvqowiy6mkwa

A polynomial time 12-approximation algorithm for restricted Santa Claus problem [article]

S Anil Kumar, N S Narayanaswamy
2020 arXiv   pre-print
To find this solution, we formulate a problem called the Extended Assignment Problem, and formulate it as an LP.  ...  In this paper, we consider the restricted case of the problem and improve the current best approximation ratio by presenting a polynomial time 12-approximation algorithm using linear programming and semi-definite  ...  the problem as a hypergraph matching problem in a suitably defined bipartite hypergraph H using the solution x * mentioned in Lemma 3.2 and then find a perfect matching in H by forming the alternating  ... 
arXiv:2007.09849v2 fatcat:2iei7dt6zbc7xfs5rufzlfiwwe

On linear and semidefinite programming relaxations for hypergraph matching

Yuk Hei Chan, Lap Chi Lau
2011 Mathematical programming  
The hypergraph matching problem is to find a largest collection of disjoint hyperedges in a hypergraph.  ...  In this paper we analyze different linear and semidefinite programming relaxations for the hypergraph matching problem, and study their connections to the local search method.  ...  The research is supported by GRF project 413609.  ... 
doi:10.1007/s10107-011-0451-5 fatcat:s3ode3xvcjacnao3yqka7yzdoq

On Linear and Semidefinite Programming Relaxations for Hypergraph Matching [chapter]

Yuk Hei Chan, Lap Chi Lau
2010 Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms  
The hypergraph matching problem is to find a largest collection of disjoint hyperedges in a hypergraph.  ...  In this paper we analyze different linear and semidefinite programming relaxations for the hypergraph matching problem, and study their connections to the local search method.  ...  The research is supported by GRF project 413609.  ... 
doi:10.1137/1.9781611973075.122 dblp:conf/soda/ChanL10 fatcat:jahiq4z7m5gqdfddq3h2ssiib4

Design and Analysis of Randomized and Approximation Algorithms (Dagstuhl Seminar 11241)

Martin Dyer, Uriel Feige, Alan M. Frieze, Marek Karpinski, Marc Herbstritt
2011 Dagstuhl Reports  
Thanks go to Mathias Hauptmann for his help in collecting abstracts of the talks and other related materials for these Proceedings.  ...  Abstracts of the presentations have been put together in this seminar proceedings document together with some links to extended abstracts and full papers.  ...  For the case T < n/r, the problem of determining F (n, r, T ) is equivalent to that of finding the maximum number of edges in an r-uniform hypergraph on n vertices with fractional matching number at most  ... 
doi:10.4230/dagrep.1.6.24 dblp:journals/dagstuhl-reports/DyerFFK11 fatcat:lb4xum4yizgo5iwrwau7d5csiy

New Constructive Aspects of the Lovasz Local Lemma [article]

Bernhard Haeupler, Barna Saha, Aravind Srinivasan
2011 arXiv   pre-print
We demonstrate our method on applications including: the first constant-factor approximation algorithm for the Santa Claus problem, as well as efficient algorithms for acyclic edge coloring, non-repetitive  ...  , and can thus be used to give efficient constructions in cases where the underlying proof applies the LLL to super-polynomially many events (or where finding a bad event that holds is computationally  ...  The first author thanks Michel Goemans and Ankur Moitra for discussing the Santa Claus problem with him in an early stage of this work.  ... 
arXiv:1001.1231v5 fatcat:z5hmdstzunbfti66dhmtcrmqse

A geometric theory for hypergraph matching

Peter Keevash, Richard Mycroft
2015 Memoirs of the American Mathematical Society  
We develop a theory for the existence of perfect matchings in hypergraphs under quite general conditions.  ...  Besides recovering previous results, we apply our theory to the solution of two open problems on hypergraph packings: the minimum degree threshold for packing tetrahedra in 3-graphs, and Fischer's conjecture  ...  Furthermore, matchings are also an important tool for many practical questions, such as the 'Santa Claus' allocation problem (see [1] ).  ... 
doi:10.1090/memo/1098 fatcat:4wdo4egtufdoxn5ctrvo6xtdtq

A Geometric Theory for Hypergraph Matching [article]

Peter Keevash, Richard Mycroft
2013 arXiv   pre-print
We develop a theory for the existence of perfect matchings in hypergraphs under quite general conditions.  ...  Besides recovering previous results, we apply our theory to the solution of two open problems on hypergraph packings: the minimum degree threshold for packing tetrahedra in 3-graphs, and Fischer's conjecture  ...  Furthermore, matchings are also an important tool for many practical questions, such as the 'Santa Claus' allocation problem (see [1] ).  ... 
arXiv:1108.1757v2 fatcat:upuiswnpafb4jhpmhmwv5mve2e

The Vessel Schedule Recovery Problem (VSRP) – A MIP model for handling disruptions in liner shipping

Berit D. Brouer, Jakob Dirksen, David Pisinger, Christian E.M. Plum, Bo Vaaben
2013 European Journal of Operational Research  
Multi-objective (MO) route selection problem is a combination of two combinatorial problems: MO shortest path problem (finding the efficient paths between the nodes to be visited) and MO traveling salesperson  ...  problem (finding the efficient tours made up of the efficient paths).  ...  The Volume-Based Storage Strategies focus on how to put goods with the highest rotation in locations most easily available to warehouseman. However, often customers buy goods in sets.  ... 
doi:10.1016/j.ejor.2012.08.016 fatcat:c27kagfnxnhjfbil2rydhjhomm

Applications of Strong Convex Relaxations to Allocation Problems

Christos Kalaitzis
2017
, or do not know how to use them.  ...  Our second contribution in this thesis is the improvement of this ratio to 1+ 2 2 + ε, for any ε > 0, for the special case of the problem where the jobs have uniform Smith ratios.  ...  The problem has also been called the Santa Claus problem, as it can be imagined that the agents are children, the items are Christmas presents, and we are Santa Claus who wants every child to receive at  ... 
doi:10.5075/epfl-thesis-7468 fatcat:t6ew3hyimvg3pgrj2emt2ns5lm

Scientific Visualization (Dagstuhl Seminar 11231) Outdoor and Large-Scale Real-World Scene Analysis. 15th Workshop Theoretic Foundations of Computer Vision

Min Chen, Hans Hagen, Charles Hansen, Arie Kaufman, Martin Dyer, Uriel Feige, Alan Frieze, Marek Karpinski, Frank Dellaert, Jan-Michael Frahm, Marc Pollefeys, Bodo Rosenhahn
2011 unpublished
Thanks go to Mathias Hauptmann for his help in collecting abstracts of the talks and other related materials for these Proceedings.  ...  We thank Annette Beyer and Angelika Mueller-von Brochowski for their continuous support and help in organizing this workshop.  ...  and for the Santa Claus problem.  ... 
fatcat:jzxttttmrvda3caw6dy4q2kw6i

st Symposium on Simplicity in Algorithms New Orleans LA, USA Co-located with The 29th ACM-SIAM Symposium on Discrete Algorithms (SODA 2018)

Raimund Seidel
2018 unpublished
In an earlier version of the proof of Theorem 3, we erroneously claimed that, conditioned on the current sampling rate being 1/2 j , edges in E t α had been sampled at that rate.  ...  Thanks to Moses Charikar, Anupam Gupta, R. Ravi and Madhur Tulsiani for helpful discussions and comments on the presentation. Acknowledgement.  ...  The first objective will be referred to as Makespan and the latter as Max-min. These problems are special cases of Scheduling on Unrelated Machines and the Santa Claus problem.  ... 
fatcat:tvuaojfsvjgfjaj7en2x4wdbhy