Related papers: Low-Depth Spatial Tree Algorithms
Multi-sector capacity expansion models play a crucial role in energy planning by providing decision support for policymaking in technology development. To ensure reliable support, these models require high technological, spatial, and…
Large spatial datasets often represent a number of spatial point processes generated by distinct entities or classes of events. When crossed with covariates, such as discrete time buckets, this can quickly result in a data set with millions…
The graph edit distance is used for comparing graphs in various domains. Due to its high computational complexity it is primarily approximated. Widely-used heuristics search for an optimal assignment of vertices based on the distance…
Merge trees are fundamental structures in topological data analysis. Interleaving distance is a widely accepted metric for comparing merge trees, with applications in visualization and scientific computing. While a greedy algorithm exists…
Multiple Tensor-Times-Matrix (Multi-TTM) is a key computation in algorithms for computing and operating with the Tucker tensor decomposition, which is frequently used in multidimensional data analysis. We establish communication lower…
We study local aggregation and graph analysis in distributed environments using the message passing model. We provide a flexible framework, where each of the nodes in a set $S$--which is a subset of all nodes in the network--can perform a…
Multi-scale spectrum sensing is proposed to overcome the cost of full network state information on the spectrum occupancy of primary users (PUs) in dense multi-cell cognitive networks. Secondary users (SUs) estimate the local spectrum…
We propose a fine-grained hypergraph model for sparse matrix-matrix multiplication (SpGEMM), a key computational kernel in scientific computing and data analysis whose performance is often communication bound. This model correctly describes…
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…
This thesis is concerned with the design of distributed algorithms for solving optimization problems. We consider networks where each node has exclusive access to a cost function, and design algorithms that make all nodes cooperate to find…
Planning under resource constraints is central to real-world decision making, yet most large language model (LLM) planners assume uniform action costs. We systematically analyze whether tree-search LLM planners are cost-aware and whether…
Researchers are exploring novel computational paradigms such as sparse coding and neuromorphic computing to bridge the efficiency gap between the human brain and conventional computers in complex tasks. A key area of focus is neuromorphic…
Decision tree algorithms have been among the most popular algorithms for interpretable (transparent) machine learning since the early 1980's. The problem that has plagued decision tree algorithms since their inception is their lack of…
We present a polynomial time dynamic programming algorithm for optimal partitions in the shortest path metric induced by a tree. This resolves, among other things, the exact complexity status of the optimal partition problems in one…
Visual localization algorithms have achieved significant improvements in performance thanks to recent advances in camera technology and vision-based techniques. However, there remains one critical caveat: all current approaches that are…
We introduce random spatial forests, a method of bagging regression trees allowing for spatial correlation. Our main contribution is the development of a computationally efficient tree building algorithm which selects each split of the tree…
Optimal transport provides a metric which quantifies the dissimilarity between probability measures. For measures supported in discrete metric spaces, finding the optimal transport distance has cubic time complexity in the size of the…
MapReduce is a widely used framework for distributed computing. Data shuffling between the Map phase and Reduce phase of a job involves a large amount of data transfer across servers, which in turn accounts for increase in job completion…
We present a scalable approach for range and $k$ nearest neighbor queries under computationally expensive metrics, like the continuous Fr\'echet distance on trajectory data. Based on clustering for metric indexes, we obtain a dynamic tree…
This paper presents a decentralized algorithm for non-convex optimization over tree-structured networks. We assume that each node of this network can solve small-scale optimization problems and communicate approximate value functions with…