Using dual approximation algorithms for scheduling problems theoretical and practical results
Journal of the ACM (JACM)
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Sublinear time algorithms for metric space problems
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
On the sum-of-squares algorithm for bin packing
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Sublinear time approximate clustering
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
A Sublinear Time Approximation Scheme for Clustering in Metric Spaces
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
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
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Optimal Time Bounds for Approximate Clustering
Machine Learning
Quick k-Median, k-Center, and Facility Location for Sparse Graphs
SIAM Journal on Computing
Approximating the Weight of the Euclidean Minimum Spanning Tree in Sublinear Time
SIAM Journal on Computing
The Complexity of Approximating the Entropy
SIAM Journal on Computing
Sublinear-time approximation algorithms for clustering via random sampling
Random Structures & Algorithms - Proceedings from the 12th International Conference “Random Structures and Algorithms”, August1-5, 2005, Poznan, Poland
Facility location in sublinear time
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Approximating average parameters of graphs
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Estimating sum by weighted sampling
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
O((log n)2) time online approximation schemes for bin packing and subset sum problems
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
SIAM Journal on Discrete Mathematics
A dense hierarchy of sublinear time approximation schemes for bin packing
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
Constant-Time approximation algorithms for the knapsack problem
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
| Hi-index | 5.23 |
The bin packing problem is defined as follows: given a set of n items with sizes 00, we present an algorithm A"@e that has sampling access to the input instance and outputs a value k such that C"o"p"t@?k@?(1+@e)@?C"o"p"t+1, where C"o"p"t is the cost of an optimal solution. It is clear that uniform sampling by itself will not allow a sublinear-time algorithm in this setting; a small number of items might constitute most of the total weight and uniform samples will not hit them. In this work we use weighted samples, where item i is sampled with probability proportional to its weight: that is, with probability w"i/@?"iw"i. In the presence of weighted samples, the approximation algorithm runs in O@?(n@?poly(1/@e))+g(1/@e) time, where g(x) is an exponential function of x. When both weighted sampling and uniform sampling are allowed, O@?(n^1^/^3@?poly(1/@e))+g(1/@e) time suffices. In addition to an approximate value to C"o"p"t, our algorithm can also output a constant-size ''template'' of a packing that can later be used to find a near-optimal packing in linear time.