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In this paper, we introduce the Fixed Topology Minimum-Length Tree with Neighborhood Problem, which aims to embed a rooted tree-shaped graph into a $d$-dimensional metric space while minimizing its total length provided that the nodes must…
We propose an extension of tree-based space-partitioning indexing structures for data with low intrinsic dimensionality embedded in a high dimensional space. We call this extension an Angle Tree. Our extension can be applied to both…
We present an axiomatic framework for analyzing the algorithmic properties of decision trees. This framework supports the classification of decision tree problems through structural and ancestral constraints within a rigorous mathematical…
Trustworthy Artificial Intelligence solutions are essential in today's data-driven applications, prioritizing principles such as robustness, safety, transparency, explainability, and privacy among others. This has led to the emergence of…
The structure of networks that provide optimal transport properties has been investigated in a variety of contexts. While many different formulations of this problem have been considered, it is recurrently found that optimal networks are…
Motion planning under differential constraints is a classic problem in robotics. To date, the state of the art is represented by sampling-based techniques, with the Rapidly-exploring Random Tree algorithm as a leading example. Yet, the…
Classification and Regression Trees (CARTs) are off-the-shelf techniques in modern Statistics and Machine Learning. CARTs are traditionally built by means of a greedy procedure, sequentially deciding the splitting predictor variable(s) and…
Decision trees are ubiquitous in machine learning for their ease of use and interpretability. Yet, these models are not typically employed in reinforcement learning as they cannot be updated online via stochastic gradient descent. We…
Decision trees are popular Classification and Regression tools and, when small-sized, easy to interpret. Traditionally, a greedy approach has been used to build the trees, yielding a very fast training process; however, controlling sparsity…
Districting-and-routing is a strategic problem aiming to aggregate basic geographical units (e.g., zip codes) into delivery districts. Its goal is to minimize the expected long-term routing cost of performing deliveries in each district…
In the theoretical study of distributed communication networks, "history trees" are a discrete structure that naturally models the concept that anonymous agents become distinguishable upon receiving different sets of messages from…
Corporations today collect data at an unprecedented and accelerating scale, making the need to run queries on large datasets increasingly important. Technologies such as columnar block-based data organization and compression have become…
Highly-optimized complex transport networks serve crucial functions in many man-made and natural systems such as power grids and plant or animal vasculature. Often, the relevant optimization functional is non-convex and characterized by…
Model trees provide an appealing way to perform interpretable machine learning for both classification and regression problems. In contrast to ``classic'' decision trees with constant values in their leaves, model trees can use linear…
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…
This paper presents a novel algorithm, called MRRT, which uses multiple rapidly-exploring random trees for fast online replanning of autonomous vehicles in dynamic environments with moving obstacles. The proposed algorithm is built upon the…
Motivated by the cabling of solar farms, we study the problem Constrained Layer Tree. At its core, it asks whether there exists a tree that connects a set of sources (the leaves) to one sink (the root) such that certain capacity constraints…
We consider a hierarchical edge-cloud architecture in which services are provided to mobile users as chains of virtual network functions. Each service has specific computation requirements and target delay performance, which require placing…
The ability of a robot to plan complex behaviors with real-time computation, rather than adhering to predesigned or offline-learned routines, alleviates the need for specialized algorithms or training for each problem instance. Monte Carlo…
Peer to peer network architecture introduces many desired features including self-scalability that led to achieving higher efficiency rate than the traditional server-client architecture. This was contributed to the highly distributed…