Related papers: Dynamic Binary Search Trees: Improved Lower Bounds…
Tackling simulation optimization problems with non-convex objective functions remains a fundamental challenge in operations research. In this paper, we propose a class of random search algorithms, called Regular Tree Search, which…
In this paper we introduce the notion of explicit worst-case bounded adaptive algorithms for applications with fixed process-completion requirements. Such applications demand that a process be guaranteed to complete within an established…
In supervised learning, decision trees are valued for their interpretability and performance. While greedy decision tree algorithms like CART remain widely used due to their computational efficiency, they often produce sub-optimal solutions…
Randomized Greedy Algorithms (RGAs) are interesting approaches to solve problems whose structures are not well understood as well as problems in combinatorial optimization which incorporate the random processes and the greedy algorithms.…
We study the connections between sorting and the binary search tree (BST) model, with an aim towards showing that the fields are connected more deeply than is currently appreciated. While any BST can be used to sort by inserting the keys…
In this experimental study we consider Steiner tree approximations that guarantee a constant approximation of ratio smaller than $2$. The considered greedy algorithms and approaches based on linear programming involve the incorporation of…
We revisit the classical problem of searching in a binary search tree (BST) using rotations, and present novel connections of this problem to a number of geometric and combinatorial structures. In particular, we show that the execution…
We tackle two long-standing problems related to re-expansions in heuristic search algorithms. For graph search, A* can require $\Omega(2^{n})$ expansions, where $n$ is the number of states within the final $f$ bound. Existing algorithms…
We introduce the lazy search tree data structure. The lazy search tree is a comparison-based data structure on the pointer machine that supports order-based operations such as rank, select, membership, predecessor, successor, minimum, and…
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…
A static binary search tree where every search starts from where the previous one ends (lazy finger) is considered. Such a search method is more powerful than that of the classic optimal static trees, where every search starts from the root…
In the dynamic set cover problem, the input is a dynamic universe of elements and a fixed collection of sets. As elements are inserted or deleted, the goal is to efficiently maintain an approximate minimum set cover. While the past decade…
Bidirectional motion planning often reduces planning time compared to its unidirectional counterparts. It requires connecting the forward and reverse search trees to form a continuous path. However, this process could fail and restart the…
In the Steiner Forest problem, we are given terminal pairs $\{s_i, t_i\}$, and need to find the cheapest subgraph which connects each of the terminal pairs together. In 1991, Agrawal, Klein, and Ravi, and Goemans and Williamson gave…
This paper investigates the problem of determining a binary-valued function through a sequence of strategically selected queries. The focus is an algorithm called Generalized Binary Search (GBS). GBS is a well-known greedy algorithm for…
We consider the problem of collaborative tree exploration posed by Fraigniaud, Gasieniec, Kowalski, and Pelc where a team of $k$ agents is tasked to collectively go through all the edges of an unknown tree as fast as possible. Denoting by…
Decision trees and randomized forests are widely used in computer vision and machine learning. Standard algorithms for decision tree induction optimize the split functions one node at a time according to some splitting criteria. This greedy…
The problem of {\em efficiently} finding the best match for a query in a given set with respect to the Euclidean distance or the cosine similarity has been extensively studied in literature. However, a closely related problem of efficiently…
We consider the online minimum cost matching problem on the line, in which there are $n$ servers and, at each of $n$ time steps, a request arrives and must be irrevocably matched to a server that has not yet been matched to, with the goal…
Classification and Regression Tree (CART), Random Forest (RF) and Gradient Boosting Tree (GBT) are probably the most popular set of statistical learning methods. However, their statistical consistency can only be proved under very…