Related papers: Sorting and Selection in Rounds with Adversarial C…
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 present novel algorithms for simulation optimization using random directions stochastic approximation (RDSA). These include first-order (gradient) as well as second-order (Newton) schemes. We incorporate both continuous-valued as well as…
We present a framework for deterministically rounding a dynamic fractional matching. Applying our framework in a black-box manner on top of existing fractional matching algorithms, we derive the following new results: (1) The first…
In this paper, we prove that with high probability, random Reed-Solomon codes approach the half-Singleton bound - the optimal rate versus error tradeoff for linear insdel codes - with linear-sized alphabets. More precisely, we prove that,…
Permutation patterns and pattern avoidance have been intensively studied in combinatorics and computer science, going back at least to the seminal work of Knuth on stack-sorting (1968). Perhaps the most natural algorithmic question in this…
We consider the problem of estimating assortment probabilities, which is common in operations management applications, including product bundling, advertising, etc. Existing approaches typically model each assortment as a category and apply…
In this paper, we present a framework based on a simple data structure and parameterized algorithms for the problems of finding items in an unsorted list of linearly ordered items based on their rank (selection) or value (search). As 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…
Traditional oversampling methods are generally employed to handle class imbalance in datasets. This oversampling approach is independent of the classifier; thus, it does not offer an end-to-end solution. To overcome this, we propose a…
In a recent breakthrough result, Balliu et al. [FOCS'19] proved a deterministic $\Omega(\min(\Delta,\log n /\log \log n))$-round and a randomized $\Omega(\min(\Delta,\log \log n/\log \log \log n))$-round lower bound for the complexity of…
We find large lower bounds for a certain family of algorithms, and prove that such bounds are limited only by natural computability arguments.
Sorting algorithms have attracted a great deal of attention and study, as they have numerous applications to Mathematics, Computer Science and related fields. In this thesis, we first deal with the mathematical analysis of the Quicksort…
In the online multiple knapsack problem, an algorithm faces a stream of items, and each item has to be either rejected or stored irrevocably in one of $n$ bins (knapsacks) of equal size. The gain of an~algorithm is equal to the sum of sizes…
This paper introduces a new comparison base stable sorting algorithm, named RS sort. RS Sort involves only the comparison of pair of elements in an array which ultimately sorts the array and does not involve the comparison of each element…
We revisit the problem of rigorously and deterministically finding elements of large order in the multiplicative group of integers modulo a natural number $N$. Solving this problem is an essential step in several recent deterministic…
We consider the problem of finding an edge in a hidden undirected graph $G = (V, E)$ with $n$ vertices, in a model where we only allowed queries that ask whether or not a subset of vertices contains an edge. We study the non-adaptive model…
When rows of an $n \times d$ matrix $A$ are given in a stream, we study algorithms for approximating the top eigenvector of the matrix ${A}^TA$ (equivalently, the top right singular vector of $A$). We consider worst case inputs $A$ but…
We consider the sample complexity of learning with adversarial robustness. Most prior theoretical results for this problem have considered a setting where different classes in the data are close together or overlapping. Motivated by some…
The problem of electing a leader from among $n$ contenders is one of the fundamental questions in distributed computing. In its simplest formulation, the task is as follows: given $n$ processors, all participants must eventually return a…
Non-dominated sorting is a computational bottleneck in Pareto-based multi-objective evolutionary algorithms (MOEAs) due to the runtime-intensive comparison operations involved in establishing dominance relationships between solution…