Bin packing via discrepancy of permutations

Authors:
Friedrich Eisenbrand;Dömötör Pálvölgyi;Thomas Rothvoß
Affiliations:
EPFL, Lausanne, Switzerland;Eötvös Loránd University (ELTE), Budapest, Hungary;EPFL, Lausanne, Switzerland
Venue:
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Year:
2011

Citing 9
Cited 4

Discrepancy of set-systems and matrices

European Journal of Combinatorics
Discrepancy theory

Handbook of combinatorics (vol. 2)
Balancing vectors and Gaussian measures of n-dimensional convex bodies

Random Structures & Algorithms
Improving the discrepancy bound for sparse matrices: better approximations for sparse lattice approximation problems

SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness
An efficient approximation scheme for the one-dimensional bin-packing problem

SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
An OPT+1 algorithm for the cutting stock problem with constant number of object lengths

IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Theoretical investigations on the modified integer round-up property for the one-dimensional cutting stock problem

Operations Research Letters
The tight bound of first fit decreasing bin-packing algorithm is FFD(I) ≤ 11/9OPT(I) + 6/9

ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies

Set covering with ordered replacement: additive and multiplicative gaps

IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
On capacitated set cover problems

APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
On the configuration-LP for scheduling on unrelated machines

ESA'11 Proceedings of the 19th European conference on Algorithms
Bin Packing via Discrepancy of Permutations

ACM Transactions on Algorithms (TALG) - Special Issue on SODA'11

Quantified Score

Hi-index	0.00

Visualization

Abstract

A well studied special case of bin packing is the 3-partition problem, where n items of size 1/4 have to be packed in a minimum number of bins of capacity one. The famous Karmarkar-Karp algorithm transforms a fractional solution of a suitable LP relaxation for this problem into an integral solution that requires at most O(log n) additional bins. The three-permutations-conjecture of Beck is the following. Given any 3 permutations on n symbols, one can color the symbols red and blue, such that in any interval of any of those permutations, the number of red and blue symbols differs only by a constant. Beck's conjecture is well known in the field of discrepancy theory. We establish a surprising connection between bin packing and Beck's conjecture: If the latter holds true, then the additive integrality gap of the 3-partition linear programming relaxation is bounded by a constant.