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There is a growing body of work on sorting and selection in models other than the unit-cost comparison model. This work is the first treatment of a natural stochastic variant of the problem where the cost of comparing two elements is a…
Traditionally, the problem of apportioning the seats of a legislative body has been viewed as a one-shot process with no dynamic considerations. While this approach is reasonable for some settings, dynamic aspects play an important role in…
In this paper, we consider the online version of the machine minimization problem (introduced by Chuzhoy et al., FOCS 2004), where the goal is to schedule a set of jobs with release times, deadlines, and processing lengths on a minimum…
Cardinality estimation algorithms receive a stream of elements whose order might be arbitrary, with possible repetitions, and return the number of distinct elements. Such algorithms usually seek to minimize the required storage and…
Sorting is one of the most basic primitives in many algorithms and data analysis tasks. Comparison-based sorting algorithms, like quick-sort and merge-sort, are known to be optimal when the outcome of each comparison is error-free. However,…
We present prior robust algorithms for a large class of resource allocation problems where requests arrive one-by-one (online), drawn independently from an unknown distribution at every step. We design a single algorithm that, for every…
In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we…
A sequential importance sampling algorithm is developed for the distribution that results when a matrix of independent, but not identically distributed, Bernoulli random variables is conditioned on a given sequence of row and column sums.…
In this paper, we study the following robust optimization problem. Given an independence system and candidate objective functions, we choose an independent set, and then an adversary chooses one objective function, knowing our choice. Our…
Read-only memory model is a classical model of computation to study time-space tradeoffs of algorithms. One of the classical results on the ROM model is that any sorting algorithm that uses O(s) words of extra space requires $\Omega…
We extend the standard online worst-case model to accommodate past experience which is available to the online player in many practical scenarios. We do this by revealing a random sample of the adversarial input to the online player ahead…
In recent years, randomized algorithms have established themselves as fundamental tools in computational linear algebra, with applications in scientific computing, machine learning, and quantum information science. Many randomized matrix…
Within the context of stochastic probing with commitment, we consider the online stochastic matching problem; that is, the one sided online bipartite matching problem where edges adjacent to an online node must be probed to determine if…
We consider online algorithms as a request-answer game. An adversary that generates input requests, and an online algorithm answers. We consider a generalized version of the game that has a buffer of limited size. The adversary loads data…
This chapter introduces the \emph{random-order model} in online algorithms. In this model, the input is chosen by an adversary, then randomly permuted before being presented to the algorithm. This reshuffling often weakens the power of the…
We propose a novel technique for algorithm-selection, applicable to optimisation domains in which there is implicit sequential information encapsulated in the data, e.g., in online bin-packing. Specifically we train two types of recurrent…
We consider the online traveling salesman problem on the real line (OLTSPL) in which a salesman begins at the origin, traveling at no faster than unit speed along the real line, and wants to serve a sequence of requests, arriving online…
For many online problems, it is known that the uniform arrival order enables the design of algorithms with much better performance guarantees than under worst-case. The quintessential example is the secretary problem. If the sequence of…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
As one of the three main pillars of fine-grained complexity theory, the 3SUM problem explains the hardness of many diverse polynomial-time problems via fine-grained reductions. Many of these reductions are either directly based on or…