Related papers: Matching on the line admits no $o(\sqrt{\log n})$-…
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…
We study the communication complexity and streaming complexity of approximating unweighted semi-matchings. A semi-matching in a bipartite graph G = (A, B, E), with n = |A|, is a subset of edges S that matches all A vertices to B vertices…
We present a new scaling algorithm for maximum (or minimum) weight perfect matching on general, edge weighted graphs. Our algorithm runs in $O(m\sqrt{n}\log(nN))$ time, $O(m\sqrt{n})$ per scale, which matches the running time of the best…
In the open online dial-a-ride problem, a single server has to deliver transportation requests appearing over time in some metric space, subject to minimizing the completion time. We improve on the best known upper bounds on the competitive…
We present a simple algorithm that estimates the cardinality $n$ of a set $V$ when allowed to sample elements of $V$ uniformly and independently at random. Our algorithm with probability $(1-\delta)$ returns a $(1\pm\epsilon)-$approximation…
In the problem of online load balancing on uniformly related machines with bounded migration, jobs arrive online one after another and have to be immediately placed on one of a given set of machines without knowledge about jobs that may…
We give an O(sqrt n log n)-query quantum algorithm for evaluating size-n AND-OR formulas. Its running time is poly-logarithmically greater after efficient preprocessing. Unlike previous approaches, the algorithm is based on a quantum walk…
In their seminal paper, Karp, Vazirani and Vazirani (STOC'90) introduce the online bipartite matching problem, and the RANKING algorithm, which admits a tight $1-\frac{1}{e}$ competitive ratio. Since its publication, the problem has…
In the Colored Bin Packing problem a sequence of items of sizes up to $1$ arrives to be packed into bins of unit capacity. Each item has one of $c\geq 2$ colors and an additional constraint is that we cannot pack two items of the same color…
In this paper we examine problems motivated by on-line financial problems and stochastic games. In particular, we consider a sequence of entirely arbitrary distinct values arriving in random order, and must devise strategies for selecting…
In the online bipartite matching with reassignments problem, an algorithm is initially given only one side of the vertex set of a bipartite graph; the vertices on the other side are revealed to the algorithm one by one, along with its…
A variant of the online knapsack problem is considered in the settings of trusted and untrusted predictions. In Unit Profit Knapsack, the items have unit profit, and it is easy to find an optimal solution offline: Pack as many of the…
We design and analyze minimax-optimal algorithms for online linear optimization games where the player's choice is unconstrained. The player strives to minimize regret, the difference between his loss and the loss of a post-hoc benchmark…
In the Online Machine Covering problem jobs, defined by their sizes, arrive one by one and have to be assigned to $m$ parallel and identical machines, with the goal of maximizing the load of the least-loaded machine. In this work, we study…
We consider the online linear optimization problem, where at every step the algorithm plays a point $x_t$ in the unit ball, and suffers loss $\langle c_t, x_t\rangle$ for some cost vector $c_t$ that is then revealed to the algorithm. Recent…
Computing lower and upper bounds on the competitive ratio of online algorithms is a challenging question: For a minimization combinatorial problem, proving a competitive ratio for a given algorithm leads to an upper bound. However computing…
This paper studies the average complexity on the number of comparisons for sorting algorithms. Its information-theoretic lower bound is $n \lg n - 1.4427n + O(\log n)$. For many efficient algorithms, the first $n\lg n$ term is easy to…
We introduce a `concrete complexity' model for studying algorithms for matching in bipartite graphs. The model is based on the "demand query" model used for combinatorial auctions. Most (but not all) known algorithms for bipartite matching…
We study the distortion of one-sided and two-sided matching problems on the line. In the one-sided case, $n$ agents need to be matched to $n$ items, and each agent's cost in a matching is their distance from the item they were matched to.…
We investigate the complexity of algorithms counting ones in different sets of operations. With addition and logical operations (but no shift) $O(\log^2(n))$ steps suffice to count ones. Parity can be computed with complexity $O(\log(n))$,…