Related papers: Online Ordinal Problems: Optimality of Comparison-…
Classical problems of sorting and searching assume an underlying linear ordering of the objects being compared. In this paper, we study a more general setting, in which some pairs of objects are incomparable. This generalization is relevant…
The advice complexity of an online problem is a measure of how much knowledge of the future an online algorithm needs in order to achieve a certain competitive ratio. Using advice complexity, we define the first online complexity class,…
In this paper we address cardinality estimation problem which is an important subproblem in query optimization. Query optimization is a part of every relational DBMS responsible for finding the best way of the execution for the given query.…
We consider the one-sided matching problem, where n agents have preferences over n items, and these preferences are induced by underlying cardinal valuation functions. The goal is to match every agent to a single item so as to maximize the…
The value maximization version of the secretary problem is the problem of hiring a candidate with the largest value from a randomly ordered sequence of candidates. In this work, we consider a setting where predictions of candidate values…
Recent years have witnessed extensive attention in binary code learning, a.k.a. hashing, for nearest neighbor search problems. It has been seen that high-dimensional data points can be quantized into binary codes to give an efficient…
We consider the problem of monotone, submodular maximization over a ground set of size $n$ subject to cardinality constraint $k$. For this problem, we introduce the first deterministic algorithms with linear time complexity; these…
Fast and high quality document clustering is an important task in organizing information, search engine results obtaining from user query, enhancing web crawling and information retrieval. With the large amount of data available and with a…
Sorting has a natural generalization where the input consists of: (1) a ground set $X$ of size $n$, (2) a partial oracle $O_P$ specifying some fixed partial order $P$ on $X$ and (3) a linear oracle $O_L$ specifying a linear order $L$ that…
The game of best choice, also known as the secretary problem, is a model for sequential decision making with many variations in the literature. Notably, the classical setup assumes that the sequence of candidate rankings is uniformly…
We study the online bipartite matching problem, introduced by Karp, Vazirani and Vazirani [1990]. For bipartite graphs with matchings of size $n$, it is known that the Ranking randomized algorithm matches at least $(1 - \frac{1}{e})n$ edges…
The 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…
Contention resolution schemes have proven to be a useful and unifying abstraction for a variety of constrained optimization problems, in both offline and online arrival models. Much of prior work restricts attention to product distributions…
Alignment techniques for LLMs rely on optimizing preference-based objectives -- where these preferences are typically elicited as ordinal, binary choices between responses. Recent work has focused on improving label quality or mitigating…
We revisit the question of reducing online learning to approximate optimization of the offline problem. In this setting, we give two algorithms with near-optimal performance in the full information setting: they guarantee optimal regret and…
Online knapsack problem is considered, where items arrive in a sequential fashion that have two attributes; value and weight. Each arriving item has to be accepted or rejected on its arrival irrevocably. The objective is to maximize the sum…
We consider maximizing a monotone submodular function under a cardinality constraint or a knapsack constraint in the streaming setting. In particular, the elements arrive sequentially and at any point of time, the algorithm has access to…
We consider the matching problem on the line with advice complexity. We give a 1-competitive online algorithm with advice complexity $n-1,$ and show that there is no 1-competitive online algorithm reading less than $n-1$ bits of advice.…
Consider a hiring process with candidates coming from different universities. It is easy to order candidates with the same background, yet it can be challenging to compare them otherwise. The latter case requires additional costly…
We introduce several generalizations of classical computer science problems obtained by replacing simpler objective functions with general submodular functions. The new problems include submodular load balancing, which generalizes load…