A Randomized Sublinear Time Parallel GCD Algorithm for the EREW PRAM

Uniform Linked Lists Contraction

We present a parallel algorithm (EREW PRAM algorithm) for linked lists contraction. We show that when we contract a linked list from size $n$ to size $n/c$ for a suitable constant $c$ we can pack the linked list into an array of size $n/d$ for a constant $1 < d\leq c$ in the time of 3 coloring the list. Thus for a set of linked lists with a total of $n$ elements and the longest list has $l$ elements our algorithm contracts them in $O(n\log i/p+(\log^{(i)}n+\log i )\log \log l+ \log l)$ time, for an arbitrary constructible integer $i$, with $p$ processors on the EREW PRAM, where $\log^{(1)} n =…

Near Optimal Parallel Algorithms for Dynamic DFS in Undirected Graphs

Depth first search (DFS) tree is a fundamental data structure for solving graph problems. The classical algorithm [SiComp74] for building a DFS tree requires $O(m+n)$ time for a given graph $G$ having $n$ vertices and $m$ edges. Recently, Baswana et al. [SODA16] presented a simple algorithm for updating DFS tree of an undirected graph after an edge/vertex update in $\tilde{O}(n)$ time. However, their algorithm is strictly sequential. We present an algorithm achieving similar bounds, that can be adopted easily to the parallel environment. In the parallel model, a DFS tree can be computed from s…

具有次线性工作量的动态常数时间并行图算法

Dynamic constant time parallel graph algorithms with sub-linear work

本研究提出CRCW PRAM模型下常数时间、次线性工作量的无向图连通性与二分性动态并行算法，验证了稀疏化技术可用于该模型的常数时间算法，工作量接近已有经典算法水平。

通过见证DAG的Lovasz局部引理的并行算法与集中界

Parallel algorithms and concentration bounds for the Lovasz Local Lemma via witness DAGs

本文提出一种基于见证DAG的并行LLL算法，在相同条件下仅用一次MIS计算，将运行时间降至$O(\log^2 n)$，并给出重采样算法的更紧运行时间界。

Simplified, stable parallel merging

This note makes an observation that significantly simplifies a number of previous parallel, two-way merge algorithms based on binary search and sequential merge in parallel. First, it is shown that the additional merge step of distinguished elements as found in previous algorithms is not necessary, thus simplifying the implementation and reducing constant factors. Second, by fixating the requirements to the binary search, the merge algorithm becomes stable, provided that the sequential merge subroutine is stable. The stable, parallel merge algorithm can easily be used to implement a stable, pa…

Minimum Linear Arrangement of Series-Parallel Graphs

We present a factor $14D^2$ approximation algorithm for the minimum linear arrangement problem on series-parallel graphs, where $D$ is the maximum degree in the graph. Given a suitable decomposition of the graph, our algorithm runs in time $O(|E|)$ and is very easy to implement. Its divide-and-conquer approach allows for an effective parallelization. Note that a suitable decomposition can also be computed in time $O(|E|\log{|E|})$ (or even $O(\log{|E|}\log^*{|E|})$ on an EREW PRAM using $O(|E|)$ processors). For the proof of the approximation ratio, we use a sophisticated charging method that …