Related papers: A Lasserre Lower Bound for the Min-Sum Single Mach…
Budget feasible mechanisms, recently initiated by Singer (FOCS 2010), extend algorithmic mechanism design problems to a realistic setting with a budget constraint. We consider the problem of designing truthful budget feasible mechanisms for…
We consider a large family of problems in which an ordering (or, more precisely, a chain of subsets) of a finite set must be chosen to minimize some weighted sum of costs. This family includes variations of Min Sum Set Cover (MSSC), several…
Initially developed for the min-knapsack problem, the knapsack cover inequalities are used in the current best relaxations for numerous combinatorial optimization problems of covering type. In spite of their widespread use, these…
We study the fundamental scheduling problem $1\mid r_j\mid\sum w_j U_j$: schedule a set of $n$ jobs with weights, processing times, release dates, and due dates on a single machine, such that each job starts after its release date and we…
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…
We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constrains. The new constrained clustering problem encompasses a number of problems and by solving it,…
The Moore-Hodgson Algorithm minimizes the number of late jobs on a single machine. That is, it finds an optimal schedule for the classical problem $1~|\;|~\sum{U_j}$. Several proofs of the correctness of this algorithm have been published.…
We investigate two new optimization problems -- minimizing a submodular function subject to a submodular lower bound constraint (submodular cover) and maximizing a submodular function subject to a submodular upper bound constraint…
We prove a general result demonstrating the power of Lagrangian relaxation in solving constrained maximization problems with arbitrary objective functions. This yields a unified approach for solving a wide class of {\em subset selection}…
This thesis explores algorithmic applications and limitations of convex relaxation hierarchies for approximating some discrete and continuous optimization problems. - We show a dichotomy of approximability of constraint satisfaction…
One of the most important open problems in machine scheduling is the problem of scheduling a set of jobs on unrelated machines to minimize the makespan. The best known approximation algorithm for this problem guarantees an approximation…
The (Non-Preemptive) Throughput Maximization problem is a natural and fundamental scheduling problem. We are given $n$ jobs, where each job $j$ is characterized by a processing time and a time window, contained in a global interval $[0,T)$,…
The $1 \mid \mid \Sigma w_j U_j$ problem asks to determine -- given $n$ jobs each with its own processing time, weight, and due date -- the minimum weighted number of tardy jobs in any single machine non-preemptive schedule for these jobs.…
We consider a recently introduced fair repetitive scheduling problem involving a set of clients, each asking for their associated job to be daily scheduled on a single machine across a finite planning horizon. The goal is to determine a job…
We consider the generalized moment problem (GMP) over the simplex and the sphere. This is a rich setting and it contains NP-hard problems as special cases, like constructing optimal cubature schemes and rational optimization. Using the…
The subject of this paper is the time complexity of approximating Knapsack, Subset Sum, Partition, and some other related problems. The main result is an $\widetilde{O}(n+1/\varepsilon^{5/3})$ time randomized FPTAS for Partition, which is…
In this work, we propose an optimization framework for estimating a sparse robust one-dimensional subspace. Our objective is to minimize both the representation error and the penalty, in terms of the l1-norm criterion. Given that the…
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function. These upper bounds are tight at the current estimate, and each iteration monotonically drives the objective…
We study the approximability of two related machine scheduling problems. In the late work minimization problem, there are identical parallel machines and the jobs have a common due date. The objective is to minimize the late work, defined…
We study the minmax optimization problem introduced in [22] for computing policies for batch mode reinforcement learning in a deterministic setting. First, we show that this problem is NP-hard. In the two-stage case, we provide two…