相关论文: A Foundation for Proving Splay is Dynamically Opti…

Motivated by recent developments in optical switching and reconfigurable network design, we study dynamic binary search trees (BSTs) in the matching model. In the classical dynamic BST model, the cost of both link traversal and basic…

We consider the following generalization of binary search in sorted arrays to tree domains. In each step of the search, an algorithm is querying a vertex $q$, and as a reply, it receives an answer, which either states that $q$ is the…

Join ordering is the NP-hard problem of selecting the most efficient order in which to evaluate joins (conjunctive, binary operators) in a database query. Because query execution performance critically depends on this choice, join ordering…

Decision tree optimization is fundamental to interpretable machine learning. The most popular approach is to greedily search for the best feature at every decision point, which is fast but provably suboptimal. Recent approaches find the…

In display advertising, advertisers want to achieve a marketing objective with constraints on budget and cost-per-outcome. This is usually formulated as an optimization problem that maximizes the total utility under constraints. The…

In FOCS 1986, Wilber proposed two combinatorial lower bounds on the operational cost of any binary search tree (BST) for a given access sequence $X \in [n]^m$. Both bounds play a central role in the ongoing pursuit of the dynamic optimality…

We analyze a tree search problem with an underlying Markov decision process, in which the goal is to identify the best action at the root that achieves the highest cumulative reward. We present a new tree policy that optimally allocates a…

This paper takes another look at the cost of traversing a binary tree using repeated splay-to-root. This was shown to cost $O(n)$ (in rotations) by Tarjan and later, in different ways, by Elmasry and others. It would be interesting to know…

How can one quickly answer the most and top popular objects at any time, given a large log stream in a system of billions of users? It is equivalent to find the mode and top-frequent elements in a dynamic array corresponding to the log…

A very simple example of an algorithmic problem solvable by dynamic programming is to maximize, over sets A in {1,2,...,n}, the objective function |A| - \sum_i \xi_i 1(i \in A,i+1 \in A) for given \xi_i > 0. This problem, with random…

It is common to encounter situations where one must solve a sequence of similar computational problems. Running a standard algorithm with worst-case runtime guarantees on each instance will fail to take advantage of valuable structure…

We study dynamic algorithms for the problem of maximizing a monotone submodular function over a stream of $n$ insertions and deletions. We show that any algorithm that maintains a $(0.5+\epsilon)$-approximate solution under a cardinality…

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…

Dynamic trees are a well-studied and fundamental building block of dynamic graph algorithms dating back to the seminal work of Sleator and Tarjan [STOC'81, (1981), pp. 114-122]. The problem is to maintain a tree subject to online edge…

We consider an autonomous navigation problem, whereby a traveler aims at traversing an environment in which an adversary tries to set an ambush. A two players zero sum game is introduced. Players' strategies are computed as random path…

This paper focuses on managing the cost of deliberation before action. In many problems, the overall quality of the solution reflects costs incurred and resources consumed in deliberation as well as the cost and benefit of execution, when…

A well-know control policy in stochastic inventory control is the (R, s, S) policy, in which inventory is raised to an order-up-to-level S at a review instant R whenever it falls below reorder-level s. To date, little or no work has been…

We develop the first fully dynamic algorithm that maintains a decision tree over an arbitrary sequence of insertions and deletions of labeled examples. Given $\epsilon > 0$ our algorithm guarantees that, at every point in time, every node…

Computational models of human language often involve combinatorial problems. For instance, a probabilistic parser may marginalize over exponentially many trees to make predictions. Algorithms for such problems often employ dynamic…

In this paper, we propose two simple yet efficient computational algorithms to obtain approximate optimal designs for multi-dimensional linear regression on a large variety of design spaces. We focus on the two commonly used optimal…