Related papers: In pursuit of the dynamic optimality conjecture
Following Poupard's study of strictly ordered binary trees with respect to two parameters, namely, "end of minimal chain" and "parent of maximum leaf" a true Tree Calculus is being developed to solve a partial difference equation system and…
We introduce two novel tree search algorithms that use a policy to guide search. The first algorithm is a best-first enumeration that uses a cost function that allows us to prove an upper bound on the number of nodes to be expanded before…
Classification trees continue to be widely adopted in machine learning applications due to their inherently interpretable nature and scalability. We propose a rolling subtree lookahead algorithm that combines the relative scalability of the…
When considering the number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate to other graphical indices in…
Most research on query optimization has centered on binary join algorithms like hash join and sort-merge join. However, recent years have seen growing interest in theoretically optimal algorithms, notably Yannakakis' algorithm. These…
While the algorithmic drawing of static trees is well-understood and well-supported by software tools, creating animations depicting how a tree changes over time is currently difficult: software support, if available at all, is not…
We present a new connection between self-adjusting binary search trees (BSTs) and heaps, two fundamental, extensively studied, and practically relevant families of data structures. Roughly speaking, we map an arbitrary heap algorithm within…
Suppose we have n keys, n access probabilities for the keys, and n+1 access probabilities for the gaps between the keys. Let h_min(n) be the minimal height of a binary search tree for n keys. We consider the problem to construct an optimal…
We consider a two-player search game on a tree $T$. One vertex (unknown to the players) is randomly selected as the target. The players alternately guess vertices. If a guess $v$ is not the target, then both players are informed in which…
This paper proposes a rapidly-exploring random trees (RRT) algorithm to solve the motion planning problem for hybrid systems. At each iteration, the proposed algorithm, called HyRRT, randomly picks a state sample and extends the search tree…
We propose a novel method for effective retrieval of multi-agent spatiotemporal tracking data. Retrieval of spatiotemporal tracking data offers several unique challenges compared to conventional text-based retrieval settings. Most notably,…
In 1996, Bodlaender showed the celebrated result that an optimal tree decomposition of a graph of bounded treewidth can be found in linear time. The algorithm is based on an algorithm of Bodlaender and Kloks that computes an optimal tree…
We study multi-finger binary search trees (BSTs), a far-reaching extension of the classical BST model, with connections to the well-studied $k$-server problem. Finger search is a popular technique for speeding up BST operations when a query…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
Many real-world problems require making sequences of decisions where the outcomes of each decision are probabilistic and uncertain, and the availability of different actions is constrained by the outcomes of previous actions. There is a…
We study sequential search without priors. Our interest lies in decision rules that are close to being optimal under each prior and after each history. We call these rules dynamically robust. The search literature employs optimal rules…
The tree inclusion problem is, given two node-labeled trees $P$ and $T$ (the ``pattern tree'' and the ``target tree''), to locate every minimal subtree in $T$ (if any) that can be obtained by applying a sequence of node insertion operations…
We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…
Research on the similarity of a graph to being a tree - called the treewidth of the graph - has seen an enormous rise within the last decade, but a practically fast algorithm for this task has been discovered only recently by Tamaki (ESA…
Many robotic tasks, such as inverse kinematics, motion planning, and optimal control, can be formulated as optimization problems. Solving these problems involves addressing nonlinear kinematics, complex contact dynamics, long-horizon…