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For a set of points in the plane, a \emph{crossing family} is a set of line segments, each joining two of the points, such that any two line segments cross. We investigate the following generalization of crossing families: a \emph{spoke…
Given a data set with many features observed in a large number of conditions, it is desirable to fuse and aggregate conditions which are similar to ease the interpretation and extract the main characteristics of the data. This paper…
Clustering is an important data mining technique that groups similar data records, recently categorical transaction clustering is received more attention. In this research, we study the problem of categorical data clustering for…
Inspired by a chessboard puzzle of Dudeney, the general position problem in graph theory asks for a largest set $S$ of vertices in a graph such that no three elements of $S$ lie on a common shortest path. The number of vertices in such a…
Generalised hypertree width ($ghw$) is a hypergraph parameter that is central to the tractability of many prominent problems with natural hypergraph structure. Computing $ghw$ of a hypergraph is notoriously hard. The decision version of the…
We formulate and optimally solve a new generalized Set Similarity Search problem, which assumes the size of the database and query sets are known in advance. By creating polylog copies of our data-structure, we optimally solve any symmetric…
Combining Large Language Models (LLMs) with heuristic search algorithms like A* holds the promise of enhanced LLM reasoning and scalable inference. To accelerate training and reduce computational demands, we investigate the coreset…
We present a learning-based approach to computing solutions for certain NP-hard problems. Our approach combines deep learning techniques with useful algorithmic elements from classic heuristics. The central component is a graph…
Let $M$ be a subset of vector space or projective space. The authors define the \emph{generalized configuration space} of $M$ which is formed by $n$-tuples of elements of $M$ where any $k$ elements of each $n$-tuple are linearly…
We study ranked enumeration of join-query results according to very general orders defined by selective dioids. Our main contribution is a framework for ranked enumeration over a class of dynamic programming problems that generalizes…
Dual encoder (DE) models, where a pair of matching query and document are embedded into similar vector representations, are widely used in information retrieval due to their simplicity and scalability. However, the Euclidean geometry of the…
While Large Language Models (LLMs) have recently shown promise in Automated Heuristic Design (AHD), existing approaches typically formulate AHD around constructive priority rules or parameterized local search guidance, thereby restricting…
This paper introduces a general modeling framework for a multi-type maximal covering location problem in which the position of facilities in different metric spaces are simultaneously decided to maximize the demand generated by a set of…
In this paper, we study a generic direct-search algorithm in which the polling directions are defined using random subspaces. Complexity guarantees for such an approach are derived thanks to probabilistic properties related to both the…
Understanding the evolution of a set of genes or species is a fundamental problem in evolutionary biology. The problem we study here takes as input a set of trees describing {possibly discordant} evolutionary scenarios for a given set of…
Recent advancements have significantly enhanced the performance of large language models (LLMs) in tackling complex reasoning tasks, achieving notable success in domains like mathematical and logical reasoning. However, these methods…
Although heuristic search is one of the most successful approaches to classical planning, this planning paradigm does not apply straightforwardly to Generalized Planning (GP). Planning as heuristic search traditionally addresses the…
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…
Hyperplane hashing aims at rapidly searching nearest points to a hyperplane, and has shown practical impact in scaling up active learning with SVMs. Unfortunately, the existing randomized methods need long hash codes to achieve reasonable…
Conjugation, or Legendre transformation, is a basic tool in convex analysis, rational mechanics, economics and optimization. It maps a function on a linear topological space into another one, defined in the dual of the linear space by…