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Building a Nest by an AutomatonApr 24 2019A robot modeled as a deterministic finite automaton has to build a structure from material available to it. The robot navigates in the infinite oriented grid $\mathbb{Z} \times \mathbb{Z}$. Some cells of the grid are full (contain a brick) and others ... More
Maximizing Online Utilization with CommitmentApr 12 2019We investigate online scheduling with commitment for parallel identical machines. Our objective is to maximize the total processing time of accepted jobs. As soon as a job has been submitted, the commitment constraint forces us to decide immediately whether ... More
The hiring problem with rank-based strategiesSep 11 2018The hiring problem is studied for general strategies based only on the relative ranking of the candidates; this includes some well known strategies studied before such as hiring above the median. We give general limit theorems for the number of hired ... More
Logarithmic regret in the dynamic and stochastic knapsack problemSep 06 2018We study a dynamic and stochastic knapsack problem in which a decision maker is sequentially presented with $n$ items with unitary rewards and independent weights that are drawn from a known continuous distribution $F$. The decision maker seeks to maximize ... More
Submodular Maximization through the Lens of Linear ProgrammingNov 30 2017The simplex algorithm for linear programming is based on the fact that any local optimum with respect to the polyhedral neighborhood is also a global optimum. We show that a similar result carries over to submodular maximization. In particular, every ... More
On estimating the alphabet size of a discrete random sourceNov 20 2017We are concerned with estimating alphabet size $N$ from a stream of symbols taken uniformly at random from that alphabet. We define and analyze a memory-restricted variant of an algorithm that have been earlier proposed for this purpose. The alphabet ... More
Iteration complexity of inexact augmented Lagrangian methods for constrained convex programmingNov 15 2017Mar 25 2018Augmented Lagrangian method (ALM) has been popularly used for solving constrained optimization problems. Practically, subproblems for updating primal variables in the framework of ALM usually can only be solved inexactly. The convergence and local convergence ... More
Uniformly bounded regret in the multi-secretary problemOct 20 2017Jun 01 2018In the secretary problem of Cayley (1875) and Moser (1956), $n$ non-negative, independent, random variables with common distribution are sequentially presented to a decision maker who decides when to stop and collect the most recent realization. The goal ... More
Randomized Similar Triangles Method: A Unifying Framework for Accelerated Randomized Optimization Methods (Coordinate Descent, Directional Search, Derivative-Free Method)Jul 26 2017In this paper, we consider smooth convex optimization problems with simple constraints and inexactness in the oracle information such as value, partial or directional derivatives of the objective function. We introduce a unifying framework, which allows ... More
A refined and asymptotic analysis of optimal stopping problems of Bruss and WeberMay 26 2017The classical secretary problem has been generalized over the years into several directions. In this paper we confine our interest to those generalizations which have to do with the more general problem of stopping on a last observation of a specific ... More
Asynchronous parallel primal-dual block update methodsMay 18 2017Recent several years have witnessed the surge of asynchronous (async-) parallel computing methods due to the extremely big data involved in many modern applications and also the advancement of multi-core machines and computer clusters. In optimization, ... More
A Framework for the Secretary Problem on the Intersection of MatroidsApr 09 2017The secretary problem became one of the most prominent online selection problems due to its numerous applications in online mechanism design. The task is to select a maximum weight subset of elements subject to given constraints, where elements arrive ... More
Accelerated first-order primal-dual proximal methods for linearly constrained composite convex programmingJun 29 2016Motivated by big data applications, first-order methods have been extremely popular in recent years. However, naive gradient methods generally converge slowly. Hence, much efforts have been made to accelerate various first-order methods. This paper proposes ... More
Hiring Secretaries over Time: The Benefit of Concurrent EmploymentApr 27 2016May 30 2017We consider a stochastic online problem where $n$ applicants arrive over time, one per time step. Upon arrival of each applicant their cost per time step is revealed, and we have to fix the duration of employment, starting immediately. This decision is ... More
Online Truthful Mechanisms for Multi-sided MarketsApr 17 2016Sep 06 2016The study of mechanisms for multi-sided markets has received an increasingly growing attention from the research community, and is motivated by the numerous examples of such markets on the web and in electronic commerce. Many of these examples represent ... More
Approximating (Unweighted) Tree Augmentation via Lift-and-Project (Part 0: $1.8+ε$ approximation for (Unweighted) TAP)Apr 04 2016We study the unweighted Tree Augmentation Problem (TAP) via the Lasserre (Sum of Squares) system. We prove an approximation guarantee of ($1.8+\epsilon$) relative to an SDP relaxation, which matches the combinatorial approximation guarantee of Even, Feldman, ... More
Online EM for Functional DataApr 02 2016A novel approach to perform unsupervised sequential learning for functional data is proposed. Our goal is to extract reference shapes (referred to as templates) from noisy, deformed and censored realizations of curves and images. Our model generalizes ... More
A Two-Phase Algorithm for Bin Stretching with Stretching Factor 1.5Jan 29 2016Aug 20 2016Online Bin Stretching is a semi-online variant of bin packing in which the algorithm has to use the same number of bins as an optimal packing, but is allowed to slightly overpack the bins. The goal is to minimize the amount of overpacking, i.e., the maximum ... More
Admissible colourings of 3-manifold triangulations for Turaev-Viro type invariantsDec 15 2015Turaev Viro invariants are amongst the most powerful tools to distinguish 3-manifolds: They are implemented in mathematical software, and allow practical computations. The invariants can be computed purely combinatorially by enumerating colourings on ... More
A Study on Splay TreesNov 10 2015We study the dynamic optimality conjecture, which predicts that splay trees are a form of universally efficient binary search tree, for any access sequence. We reduce this claim to a regular access bound, which seems plausible and might be easier to prove. ... More
Approximating (Unweighted) Tree Augmentation via Lift-and-Project, Part I: Stemless TAPAug 29 2015In Part I, we study a special case of the unweighted Tree Augmentation Problem (TAP) via the Lasserre (Sum of Squares) system. In the special case, we forbid so-called stems; these are a particular type of subtree configuration. For stemless TAP, we prove ... More
Approximating (Unweighted) Tree Augmentation via Lift-and-Project, Part IIJul 06 2015Aug 29 2015In Part II, we study the unweighted Tree Augmentation Problem (TAP) via the Lasserre (Sum~of~Squares) system. We prove that the integrality ratio of an SDP relaxation (the Lasserre tightening of an LP relaxation) is $\leq \frac{3}{2}+\epsilon$, where ... More
Online Submodular Maximization with PreemptionJan 23 2015Submodular function maximization has been studied extensively in recent years under various constraints and models. The problem plays a major role in various disciplines. We study a natural online variant of this problem in which elements arrive one-by-one ... More
Online Bin Stretching with Three BinsApr 22 2014Feb 01 2016Online Bin Stretching is a semi-online variant of bin packing in which the algorithm has to use the same number of bins as an optimal packing, but is allowed to slightly overpack the bins. The goal is to minimize the amount of overpacking, i.e., the maximum ... More
Edge Elimination in TSP InstancesFeb 28 2014The Traveling Salesman Problem is one of the best studied NP-hard problems in combinatorial optimization. Powerful methods have been developed over the last 60 years to find optimum solutions to large TSP instances. The largest TSP instance so far that ... More
Bi-Factor Approximation Algorithms for Hard Capacitated $k$-Median ProblemsDec 23 2013Apr 24 2017The $k$-Facility Location problem is a generalization of the classical problems $k$-Median and Facility Location. The goal is to select a subset of at most $k$ facilities that minimizes the total cost of opened facilities and established connections between ... More
Sufficient Conditions for Recognizing a 3-manifold GroupAug 19 2011In this work we ask when a group is a 3-manifold group, or more specifically, when does a group presentation come naturally from a Heegaard diagram for a 3-manifold? We will give some conditions for partial answers to this form of the Isomorphism Problem ... More
Optimal Lower Bounds for Projective List Update AlgorithmsFeb 11 2010Mar 08 2012The list update problem is a classical online problem, with an optimal competitive ratio that is still open, known to be somewhere between 1.5 and 1.6. An algorithm with competitive ratio 1.6, the smallest known to date, is COMB, a randomized combination ... More
A sharp threshold for minimum bounded-depth and bounded-diameter spanning trees and Steiner trees in random networksOct 27 2008May 05 2011In the complete graph on n vertices, when each edge has a weight which is an exponential random variable, Frieze proved that the minimum spanning tree has weight tending to zeta(3)=1/1^3+1/2^3+1/3^3+... as n goes to infinity. We consider spanning trees ... More