Related papers: On the Sum-of-Squares Algorithm for Bin Packing
A sum-of-squares is a polynomial that can be expressed as a sum of squares of other polynomials. Determining if a sum-of-squares decomposition exists for a given polynomial is equivalent to a linear matrix inequality feasibility problem.…
In this paper, we explore statistical versus computational trade-off to address a basic question in the application of a distributed algorithm: what is the minimal computational cost in obtaining statistical optimality? In smoothing spline…
While extensive research on query evaluation has achieved consistent improvements in the time complexity of algorithms, the space complexity of query evaluation has been largely ignored. This is a particular challenge in settings with…
This paper considers the problem of maintaining statistic aggregates over the last W elements of a data stream. First, the problem of counting the number of 1's in the last W bits of a binary stream is considered. A lower bound of…
One practical open problem is the development of a distributed algorithm that achieves near-optimal utility using only a finite (and small) buffer size for queues in a stochastic network. This paper studies utility maximization (or cost…
Online knapsack problem is considered, where items arrive in a sequential fashion that have two attributes; value and weight. Each arriving item has to be accepted or rejected on its arrival irrevocably. The objective is to maximize the sum…
The main result of this paper is a new exact algorithm computing the estimate given by the Least Trimmed Squares (LTS). The algorithm works under very weak assumptions. To prove that, we study the respective objective function using basic…
We describe an approximate dynamic programming method for stochastic control problems on infinite state and input spaces. The optimal value function is approximated by a linear combination of basis functions with coefficients as decision…
We consider the setting of online computation with advice, and study the bin packing problem and a number of scheduling problems. We show that it is possible, for any of these problems, to arbitrarily approach a competitive ratio of $1$…
We study the shared processor scheduling problem with a single shared processor where a unit time saving (weight) obtained by processing a job on the shared processor depends on the job. A polynomial-time optimization algorithm has been…
With a high probability the Sarlos randomized algorithm of 2006 outputs a nearly optimal least squares solution of a highly overdeterminedlinear system of equations. We propose its simple deterministic variation which computes such a…
Recently, Pagh presented a randomized approximation algorithm for the multiplication of real-valued matrices building upon work for detecting the most frequent items in data streams. We continue this line of research and present new {\em…
Motivated by a transit line planning problem in transportation systems, we investigate the following capacitated assignment problem under a budget constraint. Our model involves $L$ bins and $P$ items. Each bin $l$ has a utilization cost…
Optimization problems with the objective function in the form of weighted sum and linear equality constraints are considered. Given that the number of local cost functions can be large as well as the number of constraints, a stochastic…
In polynomial optimization problems, nonnegativity constraints are typically handled using the sum of squares condition. This can be efficiently enforced using semidefinite programming formulations, or as more recently proposed by Papp and…
The push-sum algorithm is probably the most important distributed averaging approach over directed graphs, which has been applied to various problems including distributed optimization. This paper establishes the explicit absolute…
Quantizing weights and activations of deep neural networks results in significant improvement in inference efficiency at the cost of lower accuracy. A source of the accuracy gap between full precision and quantized models is the…
Sampling from a dynamic discrete distribution means drawing an index with probability proportional to a mutable set of weights. Classical constant-time techniques such as the Alias Method are well suited to static distributions, but become…
We give two results concerning the power of the Sum-of-Squares(SoS)/Lasserre hierarchy. For binary polynomial optimization problems of degree $2d$ and an odd number of variables $n$, we prove that $\frac{n+2d-1}{2}$ levels of the…
Best Fit is a well known online algorithm for the bin packing problem, where a collection of one-dimensional items has to be packed into a minimum number of unit-sized bins. In a seminal work, Kenyon [SODA 1996] introduced the (asymptotic)…