Related papers: Binary Search with Distance-Dependent Costs
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,…
We consider the following generalization of the binary search problem. A search strategy is required to locate an unknown target node $t$ in a given tree $T$. Upon querying a node $v$ of the tree, the strategy receives as a reply an…
Consider the following classical search problem: given a target point $p\in \Re$, starting at the origin, find $p$ with minimum cost, where cost is defined as the distance travelled. Let $D$ be the distance of $p$ from the origin. When no…
We study a generalized binary search problem on the line and general trees. On the line (e.g., a sorted array), binary search finds a target node in $O(\log n)$ queries in the worst case, where $n$ is the number of nodes. In situations with…
We consider the problem of searching for an object on a line at an unknown distance OPT from the original position of the searcher, in the presence of a cost of d for each time the searcher changes direction. This is a generalization of the…
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…
Adaptive binary search trees are a fundamental data structure for organizing hierarchical information. Their ability to dynamically adjust to access patterns makes them particularly valuable for building responsive and efficient networked…
Consider the following generalization of the classic binary search problem: A searcher is required to find a hidden target vertex $x$ in a graph $G$. To do so, they iteratively perform queries to an oracle, each about a chosen vertex $v$.…
Beam search is a popular satisficing approach to heuristic search problems that allows one to trade increased computation time for lower solution cost by increasing the beam width parameter. We make two contributions to the study of beam…
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…
We introduce and study the general setting of weighted search in which a number of targets, each with a certain weight, are hidden in a star-like environment that consists of $m$ infinite, concurrent rays, with a common origin. A mobile…
The easy-hard-easy pattern in the difficulty of combinatorial search problems as constraints are added has been explained as due to a competition between the decrease in number of solutions and increased pruning. We test the generality of…
Search trees are commonly used to implement access operations to a set of stored keys. If this set is static and the probabilities of membership queries are known in advance, then one can precompute an optimal search tree, namely one that…
We consider the following natural generalization of Binary Search: in a given undirected, positively weighted graph, one vertex is a target. The algorithm's task is to identify the target by adaptively querying vertices. In response to…
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…
We consider the cost of general orthogonal range queries in random quadtrees. The cost of a given query is encoded into a (random) function of four variables which characterize the coordinates of two opposite corners of the query rectangle.…
We revisit the linear search problem where a robot, initially placed at the origin on an infinite line, tries to locate a stationary target placed at an unknown position on the line. Unlike previous studies, in which the robot travels along…
We consider the problem of a decision-maker searching for information on multiple alternatives when information is learned on all alternatives simultaneously. The decision-maker has a running cost of searching for information, and has to…
In query learning, the goal is to identify an unknown object while minimizing the number of "yes" or "no" questions (queries) posed about that object. A well-studied algorithm for query learning is known as generalized binary search (GBS).…
A decentralized search algorithm is a method of routing on a random graph that uses only limited, local, information about the realization of the graph. In some random graph models it is possible to define such algorithms which produce…