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In this thesis, we give new approximation algorithms for some NP-hard problems arising in resource allocation and network design. As a resource allocation problem, we study the Santa Claus problem (also known as the MaxMin Fair Allocation problem) in which ...
We show that Cutting Planes (CP) proofs are hard to find: Given an unsatisfiable formula F, It is -hard to find a CP refutation of F in time polynomial in the length of the shortest such refutation; and unless Gap-Hitting-Set admits a nontrivial algorithm, ...
A natural extension of the makespan minimization problem on unrelated machines is to allow jobs to be partially processed by different machines while incurring an arbitrary setup time. In this paper we present increasingly stronger LP-relaxations for this ...
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 inequalities yield linear ...
An integer program (IP) is a problem of the form min{f(x):Ax=b,l≤x≤u,x∈Zn}, where A∈Zm×n, b∈Zm, l,u∈Zn, and f:Zn→Z is a separable convex objective function.
The problem o ...
In this thesis we give new algorithms for two fundamental graph problems. We develop novel ways of using linear programming formulations, even exponential-sized ones, to extract structure from problem instances and to guide algorithms in making progress. S ...
Certain optimization problems in communication systems, such as limited-feedback constant-envelope beamforming or noncoherent M-ary phase-shift keying (MPSK) sequence detection, result in the maximization of a fixed-rank positive semidefinite quadratic for ...
Institute of Electrical and Electronics Engineers2014
We study the basic allocation problem of assigning resources to players to maximize fairness. This is one of the few natural problems that enjoys the intriguing status of having a better estimation algorithm than approximation algorithm. Indeed, a certain ...
Group-based sparsity models are proven instrumental in linear regression problems for recovering signals from much fewer measurements than standard compressive sensing. The main promise of these models is the recovery of ``interpretable" signals along with ...
Institute of Electrical and Electronics Engineers2016
Weighted flow time is a fundamental and very well-studied objective function in scheduling. In this paper, we study the setting of a single machine with preemptions. The input consists of a set of jobs, characterized by their processing times, release time ...
