Related papers: ParGeo: A Library for Parallel Computational Geome…
We describe a parallel, adaptive, multi-block algorithm for explicit integration of time dependent partial differential equations on two-dimensional Cartesian grids. The grid layout we consider consists of a nested hierarchy of fixed size,…
This paper studies the nucleus decomposition problem, which has been shown to be useful in finding dense substructures in graphs. We present a novel parallel algorithm that is efficient both in theory and in practice. Our algorithm achieves…
We develop a new parallel algorithm for minimizing Lipschitz, convex functions with a stochastic subgradient oracle. The total number of queries made and the query depth, i.e., the number of parallel rounds of queries, match the prior…
We present a new parallel algorithm for $k$-clique counting/listing that has polylogarithmic span (parallel time) and is work-efficient (matches the work of the best sequential algorithm) for sparse graphs. Our algorithm is based on…
Prune-and-search is an important paradigm for solving many important geometric problems. We show that the general prune-and-search technique can be implemented where the objects are given in read-only memory. As examples we consider…
In this paper, we describe efficient MapReduce simulations of parallel algorithms specified in the BSP and PRAM models. We also provide some applications of these simulation results to problems in parallel computational geometry for the…
We present a massively parallel Lagrange decomposition method for solving 0--1 integer linear programs occurring in structured prediction. We propose a new iterative update scheme for solving the Lagrangean dual and a perturbation technique…
The ability to timely process significant amounts of continuously updated spatial data is mandatory for an increasing number of applications. Parallelism enables such applications to face this data-intensive challenge and allows the devised…
We develop a novel parallel decomposition strategy for unweighted, undirected graphs, based on growing disjoint connected clusters from batches of centers progressively selected from yet uncovered nodes. With respect to similar previous…
Computing a Single-Linkage Dendrogram (SLD) is a key step in the classic single-linkage hierarchical clustering algorithm. Given an input edge-weighted tree $T$, the SLD of $T$ is a binary dendrogram that summarizes the $n-1$ clusterings…
We introduce the notion of quadratic hull of a linear code, and give some of its properties. We then show that any symmetric bilinear multiplication algorithm for a finite-dimensional algebra over a field can be obtained by…
Maintaining a $k$-core decomposition quickly in a dynamic graph has important applications in network analysis. The main challenge for designing efficient exact algorithms is that a single update to the graph can cause significant global…
In this paper, we investigate the parallelization of $k$-core decomposition, a method used in graph analysis to identify cohesive substructures and assess node centrality. Although efficient sequential algorithms exist for this task, the…
The dynamic trees problem is to maintain a forest subject to edge insertions and deletions while facilitating queries such as connectivity, path weights, and subtree weights. Dynamic trees are a fundamental building block of a large number…
We study the problem of dynamically maintaining the connected components of an undirected graph subject to edge insertions and deletions. We give the first parallel algorithm for the problem which is work-efficient, supports batches of…
Dynamic tree data structures maintain a forest while supporting insertion and deletion of edges and a broad set of queries in $O(\log n)$ time per operation. Such data structures are at the core of many modern algorithms. Recent work has…
Machine learning has been progressively generalised to operate within non-Euclidean domains, but geometrically accurate methods for learning on surfaces are still falling behind. The lack of closed-form Riemannian operators, the…
The wavelet tree (Grossi et al. [SODA, 2003]) and wavelet matrix (Claude et al. [Inf. Syst., 47:15--32, 2015]) are compact indices for texts over an alphabet $[0,\sigma)$ that support rank, select and access queries in $O(\lg \sigma)$ time.…
Convex hulls are fundamental geometric tools used in a number of algorithms. This paper presents a fast, simple to implement and robust Smart Convex Hull (S-CH) algorithm for computing the convex hull of a set of points in E3. This…
Modern trends in data collection are bringing current mainstream techniques for database query processing to their limits. Consequently, various novel approaches for efficient query processing are being actively studied. One such approach…