Related papers: Agglomerative Clustering of Growing Squares

In this work, we introduce bidirectional collision detection --- a new algorithmic tool that applies to the collision problems that arise in many isomorphism problems. For the group isomorphism problem, we show that bidirectional collision…

Many application areas collect unstructured trajectory data. In subtrajectory clustering, one is interested to find patterns in this data using a hybrid combination of segmentation and clustering. We analyze two variants of this problem…

Graph clustering is a fundamental problem in unsupervised learning, with numerous applications in computer science and in analysing real-world data. In many real-world applications, we find that the clusters have a significant high-level…

We consider problems related to finding short cycles, small cliques, small independent sets, and small subgraphs in geometric intersection graphs. We obtain a plethora of new results. For example: * For the intersection graph of $n$ line…

Clustering large datasets is a fundamental problem with a number of applications in machine learning. Data is often collected on different sites and clustering needs to be performed in a distributed manner with low communication. We would…

This paper will analyze several quadratic-time solvable problems, and will classify them into two classes: problems that are solvable in truly subquadratic time (that is, in time $O(n^{2-\epsilon})$ for some $\epsilon>0$) and problems that…

Detecting if a graph contains a $k$-Clique is one of the most fundamental problems in computer science. The asymptotically fastest algorithm runs in time $O(n^{\omega k/3})$, where $\omega$ is the exponent of Boolean matrix multiplication.…

We study the widely used hierarchical agglomerative clustering (HAC) algorithm on edge-weighted graphs. We define an algorithmic framework for hierarchical agglomerative graph clustering that provides the first efficient $\tilde{O}(m)$ time…

A recent work by Christiansen, Nowicki, and Rotenberg provides dynamic algorithms for coloring sparse graphs, concretely as a function of the arboricity alpha of the input graph. They give two randomized algorithms: O({alpha} log {alpha})…

Dense subgraphs of sparse graphs (communities), which appear in most real-world complex networks, play an important role in many contexts. Computing them however is generally expensive. We propose here a measure of similarities between…

We provide a data structure for maintaining an embedding of a graph on a surface (represented combinatorially by a permutation of edges around each vertex) and computing generators of the fundamental group of the surface, in amortized time…

We study fully dynamic algorithms for maximum matching. This is a well-studied problem, known to admit several update-time/approximation trade-offs. For instance, it is known how to maintain a 1/2-approximate matching in $\log^{O(1)} n$…

Graph isomorphism is an important computer science problem. The problem for the general case is unknown to be in polynomial time. The base algorithm for the general case works in quasi-polynomial time. The solutions in polynomial time for…

The graph isomorphism problem is theoretically interesting and also has many practical applications. The best known classical algorithms for graph isomorphism all run in time super-polynomial in the size of the graph in the worst case. An…

We introduce a novel hybrid quantum-analog algorithm to perform graph clustering that exploits connections between the evolution of dynamical systems on graphs and the underlying graph spectra. This approach constitutes a new class of…

We consider the problem of testing graph cluster structure: given access to a graph $G=(V, E)$, can we quickly determine whether the graph can be partitioned into a few clusters with good inner conductance, or is far from any such graph?…

In this paper we propose a dynamic data structure that supports efficient algorithms for updating and querying singly connected Bayesian networks (causal trees and polytrees). In the conventional algorithms, new evidence in absorbed in time…

Let $S$ be a string of length $n$ over an alphabet $\Sigma$ and let $Q$ be a subset of $\Sigma$ of size $q \geq 2$. The 'co-occurrence problem' is to construct a compact data structure that supports the following query: given an integer $w$…

Hierarchical clustering based on pairwise similarities is a common tool used in a broad range of scientific applications. However, in many problems it may be expensive to obtain or compute similarities between the items to be clustered.…

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…