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We use exponential start time clustering to design faster and more work-efficient parallel graph algorithms involving distances. Previous algorithms usually rely on graph decomposition routines with strict restrictions on the diameters of…
We describe a combinatorial approach for investigating properties of rational numbers. The overall approach rests on structural bijections between rational numbers and familiar combinatorial objects, namely rooted trees. We emphasize that…
Algorithms to generate various combinatorial structures find tremendous importance in computer science. In this paper, we begin by reviewing an algorithm proposed by Rohl that generates all unique permutations of a list of elements which…
Data processing systems impose multiple views on data as it is processed by the system. These views include spreadsheets, databases, matrices, and graphs. Associative arrays unify and simplify these different approaches into a common…
It has recently been shown that starting with a classical query algorithm (decision tree) and a guessing algorithm that tries to predict the query answers, we can design a quantum algorithm with query complexity $O(\sqrt{GT})$ where $T$ is…
Recent work has proven the existence of extreme inbreeding in a European ancestry sample taken from the contemporary UK population \cite{nature_01}. This result brings our attention again to a math problem related to inbreeding family trees…
In a seminal paper on finding large matchings in sparse random graphs, Karp and Sipser proposed two algorithms for this task. The second algorithm has been intensely studied, but due to technical difficulties, the first algorithm has…
In this paper I present a conjecture for a recursive algorithm that finds each permutation of combining two sets of objects (AKA the Shuffle Product). This algorithm provides an efficient way to navigate this problem, as each atomic…
We study parallel algorithms for correlation clustering. Each pair among $n$ objects is labeled as either "similar" or "dissimilar". The goal is to partition the objects into arbitrarily many clusters while minimizing the number of…
The intersection graph of a collection of trapezoids with corner points lying on two parallel lines is called a trapezoid graph. Using binary indexed tree data structure, we improve algorithms for calculating the size and the number of…
Decoding from the output distributions of large language models to produce high-quality text is a complex challenge in language modeling. Various approaches, such as beam search, sampling with temperature, $k-$sampling, nucleus…
An algorithm is proposed for constructing directed spanning forests of the minimum weight, in which the maximum possible degree of affinity between the minimum forests is preserved when the number of trees changes. The correctness of the…
In this paper, we study a parallel version of Galton-Watson processes for the random generation of tree-shaped structures. Random trees are useful in many situations (testing, binary search, simulation of physics phenomena,...) as attests…
Graph-based clustering methods have demonstrated the effectiveness in various applications. Generally, existing graph-based clustering methods first construct a graph to represent the input data and then partition it to generate the…
This work revisits the topic of jointly parsing constituency and dependency trees, i.e., to produce compatible constituency and dependency trees simultaneously for input sentences, which is attractive considering that the two types of trees…
We train a language model to generate LEGO-brick build sequences. While prior work has been restricted to discrete, voxel-like towers, we consider a much broader set of pieces, encompassing thousands of part types with diverse connection…
In the past thirty years, numerous algorithms for building the suffix array of a string have been proposed. In 2021, the notion of suffix array was extended from strings to DFAs, and it was shown that the resulting data structure can be…
Conditional neural text generation models generate high-quality outputs, but often concentrate around a mode when what we really want is a diverse set of options. We present a search algorithm to construct lattices encoding a massive number…
\textsc{Directed Token Sliding} asks, given a directed graph and two sets of pairwise nonadjacent vertices, whether one can reach from one set to the other by repeatedly applying a local operation that exchanges a vertex in the current set…
Hierarchical clustering studies a recursive partition of a data set into clusters of successively smaller size, and is a fundamental problem in data analysis. In this work we study the cost function for hierarchical clustering introduced by…