Related papers: Improved Parallel Construction of Wavelet Trees an…
We present the design and analysis of a near linear-work parallel algorithm for solving symmetric diagonally dominant (SDD) linear systems. On input of a SDD $n$-by-$n$ matrix $A$ with $m$ non-zero entries and a vector $b$, our algorithm…
The original description of the k-d tree recognized that rebalancing techniques, such as are used to build an AVL tree or a red-black tree, are not applicable to a k-d tree. Hence, in order to build a balanced k-d tree, it is necessary to…
Dynamic programming is a powerful technique that is, unfortunately, often inherently sequential. That is, there exists no unified method to parallelize algorithms that use dynamic programming. In this paper, we attempt to address this issue…
Given a text, rank and select queries return the number of occurrences of a character up to a position (rank) or the position of a character with a given rank (select). These queries have applications in, e.g., compression, computational…
Binary jumbled pattern matching asks to preprocess a binary string $S$ in order to answer queries $(i,j)$ which ask for a substring of $S$ that is of length $i$ and has exactly $j$ 1-bits. This problem naturally generalizes to…
Constructing a Depth First Search (DFS) tree is a fundamental graph problem, whose parallel complexity is still not settled. Reif showed parallel intractability of lex-first DFS. In contrast, randomized parallel algorithms (and more…
Parallel surrogate optimization algorithms have proven to be efficient methods for solving expensive noisy optimization problems. In this work we develop a new parallel surrogate optimization algorithm (ProSRS), using a novel tree-based…
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…
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…
``Algorithms with predictions'', or ``learning-augmented algorithms'', has proved to be an extremely useful paradigm for combining machine learning with traditional algorithms. One of the textbook settings for this is searching a sorted…
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…
For the problem of maximizing a monotone, submodular function with respect to a cardinality constraint $k$ on a ground set of size $n$, we provide an algorithm that achieves the state-of-the-art in both its empirical performance and its…
We introduce a ScatterNet that uses a parametric log transformation with Dual-Tree complex wavelets to extract translation invariant representations from a multi-resolution image. The parametric transformation aids the OLS pruning algorithm…
Using (a,b)-trees as an example, we show how to perform a parallel split with logarithmic latency and parallel join, bulk updates, intersection, union (or merge), and (symmetric) set difference with logarithmic latency and with information…
In this paper we provide a parallel algorithm that given any $n$-node $m$-edge directed graph and source vertex $s$ computes all vertices reachable from $s$ with $\tilde{O}(m)$ work and $n^{1/2 + o(1)}$ depth with high probability in $n$ .…
We propose new succinct representations of ordinal trees, which have been studied extensively. It is known that any $n$-node static tree can be represented in $2n + o(n)$ bits and a number of operations on the tree can be supported in…
In this short note, we give a novel algorithm for $O(1)$ round triangle counting in bounded arboricity graphs. Counting triangles in $O(1)$ rounds (exactly) is listed as one of the interesting remaining open problems in the recent survey of…
This is the first paper in a sequence of studies in which we introduce a new type of neural networks (NNs) -- wavelet-based neural networks (WBNNs) -- and study their properties and potential for applications. We begin this study with a…
We introduce several parallel algorithms operating on a distributed forest of adaptive quadtrees/octrees. They are targeted at large-scale applications relying on data layouts that are more complex than required for standard finite…
Previous work on Dynamic Complexity has established that there exist dynamic constant-time parallel algorithms for regular tree languages and context-free languages under label or symbol changes. However, these algorithms were not developed…