Related papers: Maximum Inner-Product Search using Tree Data-struc…
The Binary Search Tree (BST) is average in computer science which supports a compact data structure in memory and oneself even conducts a row of quick algorithms, by which people often apply it in dynamical circumstance. Besides these…
Dynamic tree data structures maintain a forest while supporting insertion and deletion of edges and a broad set of queries in $O(\log n)$ time per operation. Such data structures are at the core of many modern algorithms. Recent work has…
Given a metric space, a standard metric range search, given a query $(q,r)$, finds all points within distance $r$ of the point $q$. Suppose now we have two different metrics $d_1$ and $d_2$. A product range query $(q, r_1, r_2)$ is a point…
The branch-and-bound algorithm based on decision diagrams introduced by Bergman et al. in 2016 is a framework for solving discrete optimization problems with a dynamic programming formulation. It works by compiling a series of bounded-width…
Short spanning trees subject to additional constraints are important building blocks in various approximation algorithms. Especially in the context of the Traveling Salesman Problem (TSP), new techniques for finding spanning trees with…
Worst-case optimal join algorithms have gained a lot of attention in the database literature. We now count with several algorithms that are optimal in the worst case, and many of them have been implemented and validated in practice.…
We propose a family of search directions based on primal-dual entropy in the context of interior-point methods for linear optimization. We show that by using entropy based search directions in the predictor step of a predictor-corrector…
Maximum Inner Product Search (MIPS) for high-dimensional vectors is pivotal across databases, information retrieval, and artificial intelligence. Existing methods either reduce MIPS to Nearest Neighbor Search (NNS) while suffering from…
In this paper, we investigate adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an…
Many tasks in natural language processing, ranging from machine translation to question answering, can be reduced to the problem of matching two sentences or more generally two short texts. We propose a new approach to the problem, called…
Global optimization of decision trees is a long-standing challenge in combinatorial optimization, yet such models play an important role in interpretable machine learning. Although the problem has been investigated for several decades, only…
With XML becoming an ubiquitous language for data interoperability purposes in various domains, efficiently querying XML data is a critical issue. This has lead to the design of algebraic frameworks based on tree-shaped patterns akin to the…
In this paper we consider the problem of connected edge searching of weighted trees. It is shown that there exists a polynomial-time algorithm for finding optimal connected search strategy for bounded degree trees with arbitrary weights on…
We present an empirical analysis of data structures for approximate nearest neighbor searching. We compare the well-known optimized kd-tree splitting method against two alternative splitting methods. The first, called the sliding-midpoint…
We present an extension of Monte Carlo Tree Search (MCTS) that strongly increases its efficiency for trees with asymmetry and/or loops. Asymmetric termination of search trees introduces a type of uncertainty for which the standard upper…
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…
The combination of Monte Carlo tree search and neural networks has revolutionized online planning. As neural network approximations are often imperfect, we ask whether uncertainty estimates about the network outputs could be used to improve…
We start with a review of the pervasiveness of the nearest neighbor search problem and techniques used to solve it along with some experimental results. In the second chapter, we show reductions between two different classes of geo- metric…
We address the problem of efficiently gathering correlated data from a wired or a wireless sensor network, with the aim of designing algorithms with provable optimality guarantees, and understanding how close we can get to the known…
Planning under resource constraints is central to real-world decision making, yet most large language model (LLM) planners assume uniform action costs. We systematically analyze whether tree-search LLM planners are cost-aware and whether…