Related papers: On the Advice Complexity of Online Matching on the…
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,…
We consider the setting of online computation with advice, and study the bin packing problem and a number of scheduling problems. We show that it is possible, for any of these problems, to arbitrarily approach a competitive ratio of $1$…
We consider the online bin packing problem under the advice complexity model where the 'online constraint' is relaxed and an algorithm receives partial information about the future requests. We provide tight upper and lower bounds for the…
The online search problem is a fundamental problem in finance. The numerous direct applications include searching for optimal prices for commodity trading and trading foreign currencies. In this paper, we analyze the advice complexity of…
The bin covering problem asks for covering a maximum number of bins with an online sequence of $n$ items of different sizes in the range $(0,1]$; a bin is said to be covered if it receives items of total size at least 1. We study this…
We consider the k-server problem under the advice model of computation when the underlying metric space is sparse. On one side, we show that an advice of size {\Omega}(n) is required to obtain a 1-competitive algorithm for sequences of size…
We present a simple proof that the competitive ratio of any randomized online matching algorithm for the line is at least $\sqrt{\log_2(n\!+\!1)}/12$ for all $n=2^i\!-\!1: i\in\mathbb{N}$.
The online assignment problem plays an important role in operational research and computer science which is why immense attention has been given to improving its solution quality. Due to the incomplete information about the input, it is…
In the online hypergraph matching problem, hyperedges of size $k$ over a common ground set arrive online in adversarial order. The goal is to obtain a maximum matching (disjoint set of hyperedges). A na\"ive greedy algorithm for this…
In the online matching on the line problem, the task is to match a set of requests $R$ online to a given set of servers $S$. The distance metric between any two points in $R\,\cup\, S$ is a line metric and the objective for the online…
We analyze the competitive ratio and the advice complexity of the online unbounded knapsack problem. An instance is given as a sequence of n items with a size and a value each, and an algorithm has to decide how often to pack each item into…
In online unit clustering, points of a metric space arriving one by one must be partitioned into clusters of diameter at most 1, where the cost is the number of clusters. This paper gives linear upper and lower bounds on the advice…
We study a generalization of the advice complexity model of online computation in which the advice is provided by an untrusted source. Our objective is to quantify the impact of untrusted advice so as to design and analyze online algorithms…
Several well-studied online resource allocation problems can be formulated in terms of infinite, increasing sequences of positive values, in which each element is associated with a corresponding allocation value. Examples include problems…
We study the problem of online unweighted bipartite matching with $n$ offline vertices and $n$ online vertices where one wishes to be competitive against the optimal offline algorithm. While the classic RANKING algorithm of Karp et al.…
We study the online list update problem under the advice model of computation. Under this model, an online algorithm receives partial information about the unknown parts of the input in the form of some bits of advice generated by a…
In online minimum cost matching on the line, $n$ requests appear one by one and have to be matched immediately and irrevocably to a given set of servers, all on the real line. The goal is to minimize the sum of distances from the requests…
Recently, the first online complexity class, AOC, was introduced. The class consists of many online problems where each request must be either accepted or rejected, and the aim is to either minimize or maximize the number of accepted…
We provide simple but surprisingly useful direct product theorems for proving lower bounds on online algorithms with a limited amount of advice about the future. As a consequence, we are able to translate decades of research on randomized…
We study online algorithms with predictions using distributional advice, a type of prediction that arises when leveraging expert knowledge or historical data. To demonstrate the usefulness and versatility of this framework, we focus on the…