Related papers: Online Two-Dimensional Vector Packing with Advice
We give a $0.5368$-competitive algorithm for edge-weighted online bipartite matching. Prior to our work, the best competitive ratio was $0.5086$ due to Fahrbach, Huang, Tao, and Zadimoghaddam (FOCS 2020). They achieved their breakthrough…
Online algorithms that allow a small amount of migration or recourse have been intensively studied in the last years. They are essential in the design of competitive algorithms for dynamic problems, where objects can also depart from the…
In many problems, the inputs arrive over time, and must be dealt with irrevocably when they arrive. Such problems are online problems. A common method of solving online problems is to first solve the corresponding linear program, and then…
We study the well-known two-dimensional strip packing problem. Given is a set of rectangular axis-parallel items and a strip of width $W$ with infinite height. The objective is to find a packing of these items into the strip, which…
In evaluating an algorithm, worst-case analysis can be overly pessimistic. Average-case analysis can be overly optimistic. An intermediate approach is to show that an algorithm does well on a broad class of input distributions. Koutsoupias…
We study three classical online problems -- $k$-server, $k$-taxi, and chasing size $k$ sets -- through a lens of smoothed analysis. Our setting allows request locations to be adversarial up to small perturbations, interpolating between…
Clique clustering is the problem of partitioning the vertices of a graph into disjoint clusters, where each cluster forms a clique in the graph, while optimizing some objective function. In online clustering, the input graph is given one…
This paper consider considers the problem of locating a two dimensional target from range-measurements containing outliers. Assuming that the number of outlier is known, we formulate the problem of minimizing inlier losses while ignoring…
There is a rising interest for studying the online benchmark as an alternative of the classical offline benchmark in online stochastic settings. Ezra, Feldman, Gravin, and Tang (SODA 2023) introduced the notion of order-competitive ratio,…
We consider the problem of solving packing/covering LPs online, when the columns of the constraint matrix are presented in random order. This problem has received much attention and the main focus is to figure out how large the right-hand…
In the model of online caching with machine learned advice, introduced by Lykouris and Vassilvitskii, the goal is to solve the caching problem with an online algorithm that has access to next-arrival predictions: when each input element…
This article presents a simplification of Zadimoghaddam's algorithm for the edge-weighted online bipartite matching problem, under the online primal dual framework. In doing so, we obtain an improved competitive ratio of $0.514$. We first…
We consider a two-way trading problem, where investors buy and sell a stock whose price moves within a certain range. Naturally they want to maximize their profit. Investors can perform up to $k$ trades, where each trade must involve the…
Online matching has received significant attention over the last 15 years due to its close connection to Internet advertising. As the seminal work of Karp, Vazirani, and Vazirani has an optimal (1 - 1/e) competitive ratio in the standard…
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…
In several applications of real-time matching of demand to supply in online marketplaces, the platform allows for some latency to batch the demand and improve the efficiency. Motivated by these applications, we study the optimal trade-off…
We consider max-weighted matching with costs for learning the weights, modeled as a "Pandora's Box" on each endpoint of an edge. Each vertex has an initially-unknown value for being matched to a neighbor, and an algorithm must pay some cost…
We study the uniform $2$-dimensional vector multiple knapsack (2VMK) problem, a natural variant of multiple knapsack arising in real-world applications such as virtual machine placement. The input for 2VMK is a set of items, each associated…
We consider the classical online bipartite matching problem in the probe-commit model. In this problem, when an online vertex arrives, its edges must be probed to determine if they exist, based on known edge probabilities. A probing…
We introduce the Online Unbounded Knapsack Problem with Removal, a variation of the well-known Online Knapsack Problem. Items, each with a weight and value, arrive online and an algorithm must decide on whether or not to pack them into a…