Probabilistic counting algorithms for data base applications
Journal of Computer and System Sciences
Randomized algorithms
The space complexity of approximating the frequency moments
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
On the sum-of-squares algorithm for bin packing
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
On the closest string and substring problems
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A Self Organizing Bin Packing Heuristic
ALENEX '99 Selected papers from the International Workshop on Algorithm Engineering and Experimentation
Estimating the weight of metric minimum spanning trees in sublinear-time
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Approximating the Minimum Spanning Tree Weight in Sublinear Time
SIAM Journal on Computing
Approximating the Weight of the Euclidean Minimum Spanning Tree in Sublinear Time
SIAM Journal on Computing
Sublinear Geometric Algorithms
SIAM Journal on Computing
A sublinear-time approximation scheme for bin packing
Theoretical Computer Science
Hi-index | 0.00 |
The bin packing problem is to find the minimum number of bins of size one to pack a list of items with sizes a 1 ,…, a n in (0,1]. Using uniform sampling, which selects a random element from the input list each time, we develop a randomized $O({n(\log\log n)\over \sum_{i=1}^n a_i}+({1\over \epsilon})^{O({1\over\epsilon})})$ time (1+ε )-approximation scheme for the bin packing problem. We show that every randomized algorithm with uniform random sampling needs $\Omega({n\over \sum_{i=1}^n a_i})$ time to give an (1+ε )-approximation. For each function s (n ): N →N , define ∑(s (n )) to be the set of all bin packing problems with the sum of item sizes equal to s (n ). We show that ∑(n b ) is NP-hard for every b ∈(0,1]. This implies a dense sublinear time hierarchy of approximation schemes for a class of NP-hard problems, which are derived from the bin packing problem. We also show a randomized streaming approximation scheme for the bin packing problem such that it needs only constant updating time and constant space, and outputs an (1+ε )-approximation in $({1\over \epsilon})^{O({1\over\epsilon})}$ time. Let S (δ )-bin packing be the class of bin packing problems with each input item of size at least δ . This research also gives a natural example of NP-hard problem (S (δ )-bin packing) that has a constant time approximation scheme, and a constant time and space sliding window streaming approximation scheme, where δ is a positive constant.