Related papers: The landscape of bounds for binary search trees
In the particular case we have insertions/deletions at the tail of a given set S of $n$ one-dimensional elements, we present a simpler and more concrete algorithm than that presented in [Anderson, 2007] achieving the same (but also…
Contextual bandits are a core technology for personalized mobile health interventions, where decision-making requires adapting to complex, non-linear user behaviors. While Thompson Sampling (TS) is a preferred strategy for these problems,…
Continuing the recent trend, in this article we design several space-efficient algorithms for two well-known graph search methods. Both these search methods share the same name {\it breadth-depth search} (henceforth {\sf BDS}), although…
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 neighborhood tree induced by alternating the use of different neighborhood structures within a local search descent. We investigate the issue of designing a search strategy operating at the neighborhood tree level by…
Consider the task of performing a sequence of searches in a binary search tree. After each search, we allow an algorithm to arbitrarily restructure the tree. The cost of executing the task is the sum of the time spent searching and the time…
We present a formal framework for proving the correctness of set implementations backed by binary-search-tree (BST) and linked lists, which are often difficult to prove correct using automation. This is because many concurrent set…
Recent research suggests that tree search algorithms (e.g. Monte Carlo Tree Search) can dramatically boost LLM performance on complex mathematical reasoning tasks. However, they often require more than 10 times the computational resources…
We present space-efficient parallel strategies for two fundamental combinatorial search problems, namely, backtrack search and branch-and-bound, both involving the visit of an $n$-node tree of height $h$ under the assumption that a node can…
Behavior Trees (BTs) are becoming a popular tool to model the behaviors of autonomous agents in the computer game and the robotics industry. One of the key advantages of BTs lies in their composability, where complex behaviors can be built…
In recent years, significant progress has been made on algorithms for learning optimal decision trees, primarily in the context of binary features. Extending these methods to continuous features remains substantially more challenging due to…
This paper presents a general technique for optimally transforming any dynamic data structure that operates on atomic and indivisible keys by constant-time comparisons, into a data structure that handles unbounded-length keys whose…
A dynamic forest data structure maintains a forest (and associated data like edge weights) under edge insertions and deletions. Dynamic forests are widely used to solve online and offline graph problems. Well-known examples of dynamic…
This paper considers the classic Online Steiner Forest problem where one is given a (weighted) graph $G$ and an arbitrary set of $k$ terminal pairs $\{\{s_1,t_1\},\ldots ,\{s_k,t_k\}\}$ that are required to be connected. The goal is to…
The performance of acquisition functions for Bayesian optimisation to locate the global optimum of continuous functions is investigated in terms of the Pareto front between exploration and exploitation. We show that Expected Improvement…
We consider the reachability problem for timed automata. A standard solution to this problem involves computing a search tree whose nodes are abstractions of zones. For efficiency reasons, they are parametrized by the maximal lower and…
We study reward maximisation in a wide class of structured stochastic multi-armed bandit problems, where the mean rewards of arms satisfy some given structural constraints, e.g. linear, unimodal, sparse, etc. Our aim is to develop methods…
We investigate the complexity of local search based on steepest ascent. We show that even when all variables have domains of size two and the underlying constraint graph of variable interactions has bounded treewidth (in our construction,…
The Greedy algorithm is the simplest heuristic in sequential decision problem that carelessly takes the locally optimal choice at each round, disregarding any advantages of exploring and/or information gathering. Theoretically, it is known…
While modern biotechnologies allow synthesizing new proteins and function measurements at scale, efficiently exploring a protein sequence space and engineering it remains a daunting task due to the vast sequence space of any given protein.…