Related papers: BFS versus DFS for random targets in ordered trees
The purpose of this report is to explain how the textbook breadth-first search algorithm (BFS) can be modified in order to also create a compact representation of all shortest paths connecting a single source node to all the nodes reachable…
Large Language Models have excelled in remarkable reasoning capabilities with advanced prompting techniques, but they fall short on tasks that require exploration, strategic foresight, and sequential decision-making. Recent works propose to…
We derive ensembles of decision trees through a nonparametric Bayesian model, allowing us to view random forests as samples from a posterior distribution. This insight provides large gains in interpretability, and motivates a class of…
Depth first search is a fundamental graph problem having a wide range of applications. For a graph $G=(V,E)$ having $n$ vertices and $m$ edges, the DFS tree can be computed in $O(m+n)$ using $O(m)$ space where $m=O(n^2)$. In the streaming…
We present a new algorithm for maintaining a DFS tree of an arbitrary directed graph under any sequence of edge insertions. Our algorithm requires a total of $O(m\cdot n)$ time in the worst case to process a sequence of edge insertions,…
We attempt to determine the best order and search algorithm to store $n$ comparable data items in an array, $A$, of length $n$ so that we can, for any query value, $x$, quickly find the smallest value in $A$ that is greater than or equal to…
Despite the latest prevailing success of deep neural networks (DNNs), several concerns have been raised against their usage, including the lack of intepretability the gap between DNNs and other well-established machine learning models, and…
Graph searches and their respective search trees are widely used in algorithmic graph theory. The problem whether a given spanning tree can be a graph search tree has been considered for different searches, graph classes and search tree…
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…
Random search methods are widely used for global optimization due to their theoretical generality and implementation simplicity. This paper proposes a depth-first directional search (DFDS) algorithm for globally solving nonconvex…
Gaussian smoothing (GS) is a derivative-free optimization (DFO) algorithm that estimates the gradient of an objective using perturbations of the current parameters sampled from a standard normal distribution. We generalize it to sampling…
Graphs and their traversal is becoming significant as it is applicable to various areas of mathematics, science and technology. Various problems in fields as varied as biochemistry (genomics), electrical engineering (communication…
Decision Tree (DT) Learning is a fundamental problem in Interpretable Machine Learning, yet it poses a formidable optimisation challenge. Practical algorithms have recently emerged, primarily leveraging Dynamic Programming and Branch &…
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…
Bayesian Neural Networks (BNNs) offer a mathematically grounded framework to quantify the uncertainty of model predictions but come with a prohibitive computation cost for both training and inference. In this work, we show a novel network…
Popular Monte-Carlo tree search (MCTS) algorithms for online planning, such as epsilon-greedy tree search and UCT, aim at rapidly identifying a reasonably good action, but provide rather poor worst-case guarantees on performance improvement…
Context: One of the black arts of data mining is learning the magic parameters which control the learners. In software analytics, at least for defect prediction, several methods, like grid search and differential evolution (DE), have been…
Geodesic distance, sometimes called shortest path length, has proven useful in a great variety of applications, such as information retrieval on networks including treelike networked models. Here, our goal is to analytically determine the…
First passage time (FPT) theory is often used to estimate timescales in cellular and molecular biology. While the overwhelming majority of studies have focused on the time it takes a given single Brownian searcher to reach a target,…
In the big data era, graph computing is widely used to exploit the hidden value in real-world graphs in various scenarios such as social networks, knowledge graphs, web searching, and recommendation systems. However, the random memory…