Related papers: Fast Rational Search via Stern-Brocot Tree
An algorithm for structured database searching is presented and used to solve the set partition problem. O(n) oracle calls are required in order to obtain a solution, but the probability that this solution is optimal decreases exponentially…
Evolutionary Algorithms are naturally inspired approximation optimisation algorithms that usually interfere with science problems when common mathematical methods are unable to provide a good solution or finding the exact solution requires…
The linear search problem, informally known as the cow path problem, is one of the fundamental problems in search theory. In this problem, an immobile target is hidden at some unknown position on an unbounded line, and a mobile searcher,…
In search problems, a mobile searcher seeks to locate a target that hides in some unknown position of the environment. Such problems are typically considered to be of an on-line nature, in that the input is unknown to the searcher, and the…
Algorithms for efficiently finding optimal alphabetic decision trees -- such as the Hu-Tucker algorithm -- are well established and commonly used. However, such algorithms generally assume that the cost per decision is uniform and thus…
We consider linear search for an escaping target whose speed and initial position are unknown to the searcher. A searcher (an autonomous mobile agent) is initially placed at the origin of the real line and can move with maximum speed $1$ in…
Existing retrieval benchmarks primarily consist of information-seeking queries (e.g., aggregated questions from search engines) where keyword or semantic-based retrieval is usually sufficient. However, many complex real-world queries…
Consider an agent exploring an unknown graph in search of some goal state. As it walks around the graph, it learns the nodes and their neighbors. The agent only knows where the goal state is when it reaches it. How do we reach this goal…
We consider the following generalization of the classic Binary Search Problem: a searcher is required to find a hidden target vertex $x$ in a graph $G$, by iteratively performing queries about vertices. A query to $v$ incurs a cost $c(v,…
Consider the following generalization of the classic binary search problem: a searcher is required to find a hidden vertex $x$ in a tree $T$. To do so, they iteratively perform queries to an oracle, each about a chosen vertex $v$. After…
Given a hypergraph with uncertain node weights following known probability distributions, we study the problem of querying as few nodes as possible until the identity of a node with minimum weight can be determined for each hyperedge.…
We study learning-augmented binary search trees (BSTs) via Treaps with carefully designed priorities. The result is a simple search tree in which the depth of each item $x$ is determined by its predicted weight $w_x$. Specifically, each…
In the field of algorithmic analysis, one of the more well-known exercises is the subset sum problem. That is, given a set of integers, determine whether one or more integers in the set can sum to a target value. Aside from the brute-force…
We consider the quantum complexities of the following three problems: searching an ordered list, sorting an un-ordered list, and deciding whether the numbers in a list are all distinct. Letting N be the number of elements in the input list,…
In this paper we study the properties of the \emph{Triangular tree}, a complete tree of rational pairs introduced in \cite{cas}, in analogy with the main properties of the Farey tree (or Stern-Brocot tree). To our knowledge the Triangular…
Sparse decision tree optimization has been one of the most fundamental problems in AI since its inception and is a challenge at the core of interpretable machine learning. Sparse decision tree optimization is computationally hard, and…
The process of discovery requires active exploration -- the act of collecting new and informative data. However, efficient autonomous exploration remains a major unsolved problem. The dominant paradigm addresses this challenge by using…
With the rapid development of mobile computing and Web services, a huge amount of data with spatial and temporal information have been collected everyday by smart mobile terminals, in which an object is described by its spatial information…
One of the basic tasks for Bayesian networks (BNs) is that of learning a network structure from data. The BN-learning problem is NP-hard, so the standard solution is heuristic search. Many approaches have been proposed for this task, but…
We formulate and study a statistical version of Katona's two-round search problem of finding at least one excellent element in a set. A population of $n$ elements is considered, where each element is independently excellent with probability…