Related papers: An Algorithm for Bichromatic Sorting with Polylog …
We consider the problem of partial order production: arrange the elements of an unknown totally ordered set T into a target partially ordered set S, by comparing a minimum number of pairs in T. Special cases include sorting by comparisons,…
This paper studies an online selection problem, where a seller seeks to sequentially sell multiple copies of an item to arriving buyers. We consider an adversarial setting, making no modeling assumptions about buyers' valuations for the…
We consider online algorithms under both the competitive ratio criteria and the regret minimization one. Our main goal is to build a unified methodology that would be able to guarantee both criteria simultaneously. For a general class of…
We introduce new stable natural merge sort algorithms, called $2$-merge sort and $\alpha$-merge sort. We prove upper and lower bounds for several merge sort algorithms, including Timsort, Shivers' sort, $\alpha$-stack sorts, and our new…
We discuss one of the most fundamental scheduling problem of processing jobs on a single machine to minimize the weighted flow time (weighted response time). Our main result is a $O(\log P)$-competitive algorithm, where $P$ is the…
Combinatorial bilevel congestion pricing (CBCP), a variant of the mixed (continuous/discrete) network design problems, seeks to minimize the total travel time experienced by all travelers in a road network, by strategically selecting toll…
This paper improves and in two cases nearly settles, up to logarithmically lower-order factors, the deterministic complexity of some of the most central problems in distributed graph algorithms, which have been studied for over three…
In \emph{Online Sorting}, an array of $n$ initially empty cells is given. At each time step $t$, an element $x_t \in [0,1]$ arrives and must be placed irrevocably into an empty cell without any knowledge of future arrivals. We aim to…
In \emph{Online Sorting}, an array of $n$ initially empty cells is given. At each time step $t$, an element $x_t \in [0,1]$ arrives and must be placed irrevocably into an empty cell without any knowledge of future arrivals. We aim to…
Circuit routing has been a historically challenging problem in designing electronic systems such as very large-scale integration (VLSI) and printed circuit boards (PCBs). The main challenge is that connecting a large number of electronic…
Online bipartite matching has been extensively studied. In the unweighted setting, Karp et al. gave an optimal $(1 - 1/e)$-competitive randomized algorithm. In the weighted setting, optimal algorithms have been achieved only under…
Chjara, breeder in Carg{\`e}se, has n wild pigs. She would like to sort her herd by weight to better meet the demands of her buyers. Each beast has a distinct weight, alas unknown to Chjara. All she has at her disposal is a Roberval scale,…
The Balanced Connected Subgraph problem (BCS) was recently introduced by Bhore et al. (CALDAM 2019). In this problem, we are given a graph $G$ whose vertices are colored by red or blue. The goal is to find a maximum connected subgraph of…
Scalable real-time assortment optimization has become essential in e-commerce operations due to the need for personalization and the availability of a large variety of items. While this can be done when there are simplistic assortment…
Sorting and hashing are two completely different concepts in computer science, and appear mutually exclusive to one another. Hashing is a search method using the data as a key to map to the location within memory, and is used for rapid…
We study packing LPs in an online model where the columns are presented to the algorithm in random order. This natural problem was investigated in various recent studies motivated, e.g., by online ad allocations and yield management where…
In this paper we consider clustering problems in which each point is endowed with a color. The goal is to cluster the points to minimize the classical clustering cost but with the additional constraint that no color is over-represented in…
In this paper, we introduce a family of sequential decision-making problems, collectively termed the Keychain Problem, that involve exploring a set of actions to maximize expected payoff when only a subset of actions are available in each…
Ranking is one of the most fundamental problems in machine learning with applications in many branches of computer science such as: information retrieval systems, recommendation systems, machine translation and computational biology.…
QuickSelect (aka Find), introduced by Hoare (1961), is a randomized algorithm for selecting a specified order statistic from an input sequence of $n$ objects, or rather their identifying labels usually known as keys. The keys can be numeric…