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The kd-tree is a fundamental tool in computer science. Among others, an application of the kd-tree search (oct-tree method) to fast evaluation of particle interactions and neighbor search is highly important since computational complexity…
This paper presents a detailed comparison of a recently proposed algorithm for optimizing decision trees, tree alternating optimization (TAO), with other popular, established algorithms. We compare their performance on a number of…
The computation of feedback control using Dynamic Programming equation is a difficult task due the curse of dimensionality. The tree structure algorithm is one the methods introduced recently that mitigate this problem. The method computes…
Dual-tree algorithms are a widely used class of branch-and-bound algorithms. Unfortunately, developing dual-tree algorithms for use with different trees and problems is often complex and burdensome. We introduce a four-part logical split:…
This PhD thesis summarizes research works on the design of exact algorithms that provide a worst-case (time or space) guarantee for NP-hard scheduling problems. Both theoretical and practical aspects are considered with three main results…
The independence number of a tree decomposition is the maximum of the independence numbers of the subgraphs induced by its bags. The tree-independence number of a graph is the minimum independence number of a tree decomposition of it.…
We present TREVR (Tree-based REVerse Ray Tracing), a general algorithm for computing the radiation field, including absorption, in astrophysical simulations. TREVR is designed to handle large numbers of sources and absorbers; it is based on…
The truncation scheme dependence of the exact renormalization group equations is investigated for scalar field theories in three dimensions. The exponents are numerically estimated to the next-to-leading order of the derivative expansion.…
The focus of this paper is the analysis of real-time systems with recursion, through the development of good theoretical techniques which are implementable. Time is modeled using clock variables, and recursion using stacks. Our technique…
A tremendous range of design tasks in materials, physics, and biology can be formulated as finding the optimum of an objective function depending on many parameters without knowing its closed-form expression or the derivative. Traditional…
The authors recently gave an $n^{O(\log\log n)}$ time membership query algorithm for properly learning decision trees under the uniform distribution (Blanc et al., 2021). The previous fastest algorithm for this problem ran in $n^{O(\log…
Energy systems optimization problems are complex due to strongly non-linear system behavior and multiple competing objectives, e.g. economic gain vs. environmental impact. Moreover, a large number of input variables and different variable…
Avraham et al. [AFK+15] presented an alternative approach to parametric search, called \emph{bifurcation}, that performs faster under certain circumstances. Intuitively, when the underlying decider execution can be rolled back cheaply and…
We present a comprehensive classical and parameterized complexity analysis of decision tree pruning operations, extending recent research on the complexity of learning small decision trees. Thereby, we offer new insights into the…
In this paper, we consider tree decompositions, branch decompositions, and clique decompositions. We improve the running time of dynamic programming algorithms on these graph decompositions for a large number of problems as a function of…
We present an algorithm for the Merkle tree traversal problem which combines the efficient space-time trade-off from the fractal Merkle tree [3] and the space efficiency from the improved log space-time Merkle trees traversal [8]. We give…
The problem of constructing optimal factoring automata arises in the context of unification factoring for the efficient execution of logic programs. Given an ordered set of $n$ strings of length $m$, the problem is to construct a trie-like…
We present a new algorithm to rapidly and optimally compute power spectra. This new algorithm is based on a generalization of iterative multigrid, and has computational cost O(N log N), compared to the standard brute force approach which…
Tree-based models have proven to be an effective solution for web ranking as well as other problems in diverse domains. This paper focuses on optimizing the runtime performance of applying such models to make predictions, given an…
We introduce our new binary tree code for neighbour search and gravitational force calculations in an N-particle system. The tree is built in a "top-down" fashion by "recursive coordinate bisection" where on each tree level we split the…