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In this paper we develop optimal algorithms in the binary-forking model for a variety of fundamental problems, including sorting, semisorting, list ranking, tree contraction, range minima, and ordered set union, intersection and difference.…

Any function can be constructed using a hierarchy of simpler functions through compositions. Such a hierarchy can be characterized by a binary rooted tree. Each node of this tree is associated with a function which takes as inputs two…

Conventionally, random forests are built from "greedy" decision trees which each consider only one split at a time during their construction. The sub-optimality of greedy implementation has been well-known, yet mainstream adoption of more…

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…

The ability to explain why a machine learning model arrives at a particular prediction is crucial when used as decision support by human operators of critical systems. The provided explanations must be provably correct, and preferably…

Numerous machine learning algorithms contain pairwise statistical problems at their core---that is, tasks that require computations over all pairs of input points if implemented naively. Often, tree structures are used to solve these…

Industrial robots can solve very complex tasks in controlled environments, but modern applications require robots able to operate in unpredictable surroundings as well. An increasingly popular reactive policy architecture in robotics is…

We introduce a novel interpretable tree based algorithm for prediction in a regression setting. Our motivation is to estimate the unknown regression function from a functional decomposition perspective in which the functional components…

Ordinals can help prove termination for dependently typed programs. Brouwer trees are a particular ordinal notation that make it very easy to assign sizes to higher order data structures. They extend natural numbers with a limit…

In the Properly Colored Spanning Tree problem, we are given an edge-colored undirected graph and the goal is to find a spanning tree in which any two adjacent edges have distinct colors. Since finding such a tree is NP-hard in general,…

Modern highly-concurrent search data structures, such as search trees, obtain multi-core scalability and performance by having operations traverse the data structure without any synchronization. As a result, however, these algorithms are…

The kernel method is a potential approach to analyzing structured data such as sequences, trees, and graphs; however, unordered trees have not been investigated extensively. Kimura et al. (2011) proposed a kernel function for unordered…

We show that time complexity analysis of higher-order functional programs can be effectively reduced to an arguably simpler (although computationally equivalent) verification problem, namely checking first-order inequalities for validity.…

Efficient implementations of sets and maps (dictionaries) are important in computer science, and balanced binary search trees are the basis of the best practical implementations. Pedagogically, however, they are often quite complicated,…

We introduce a framework for automatically choosing data structures to support efficient computation of analytical workloads. Our contributions are twofold. First, we introduce a novel low-level intermediate language that can express the…

The theory of regular cost functions is a quantitative extension to the classical notion of regularity. A cost function associates to each input a non-negative integer value (or infinity), as opposed to languages which only associate to…

We develop a theoretical framework for the analysis of oblique decision trees, where the splits at each decision node occur at linear combinations of the covariates (as opposed to conventional tree constructions that force axis-aligned…

This paper presents a new approach to statistical similarity assessment based on sequence alignment. The algorithm performs mutual matching of two random sequences by successively searching for common elements and by applying sequence…

Full binary trees naturally represent commutative non-associative products. There are many important examples of these products: finite-precision floating-point addition and NAND gates, among others. Balance in such a tree is highly…

Tree kernels have been proposed to be used in many areas as the automatic learning of natural language applications. In this paper, we propose a new linear time algorithm based on the concept of weighted tree automata for SubTree kernel…