Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA Distributed-Memory Algorithm for Computing a Heavy-Weight Perfect Matching on Bipartite Graphs
64
0
0.0
(
0
)
Added by
Ariful Azad
Publication date
2018
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
We design and implement an efficient parallel algorithm for finding a perfect matching in a weighted bipartite graph such that weights on the edges of the matching are large. This problem differs from the maximum weight matching problem, for which scalable approximation algorithms are known. It is primarily motivated by finding good pivots in scalable sparse direct solvers before factorization. Due to the lack of scalable alternatives, distributed solvers use sequential implementations of maximum weight perfect matching algorithms, such as those available in MC64. To overcome this limitation, we propose a fully parallel distributed memory algorithm that first generates a perfect matching and then iteratively improves the weight of the perfect matching by searching for weight-increasing cycles of length four in parallel. For most practical problems the weights of the perfect matchings generated by our algorithm are very close to the optimum. An efficient implementation of the algorithm scales up to 256 nodes (17,408 cores) on a Cray XC40 supercomputer and can solve instances that are too large to be handled by a single node using the sequential algorithm.
rate research
Read More
In a recent paper, Beniamini and Nisan gave a closed-form formula for the unique multilinear polynomial for the Boolean function determining whether a given bipartite graph $G subseteq K_{n,n}$ has a perfect matching, together with an efficient algorithm for computing the coefficients of the monomials of this polynomial. We give the following generalization: Given an arbitrary non-negative weight function $w$ on the edges of $K_{n,n}$, consider its set of minimum weight perfect matchings. We give the real multilinear polynomial for the Boolean function which determines if a graph $G subseteq K_{n,n}$ contains one of these minimum weight perfect matchings.
Scripting languages such as Python and R have been widely adopted as tools for the productive development of scientific software because of the power and expressiveness of the languages and available libraries. However, deploying scripted applications on large-scale parallel computer systems such as the IBM Blue Gene/Q or Cray XE6 is a challenge because of issues including operating system limitations, interoperability challenges, parallel filesystem overheads due to the small file system accesses common in scripted approaches, and other issues. We present here a new approach to these problems in which the Swift scripting system is used to integrate high-level scripts written in Python, R, and Tcl, with native code developed in C, C++, and Fortran, by linking Swift to the library interfaces to the script interpreters. In this approach, Swift handles data management, movement, and marshaling among distributed-memory processes without direct user manipulation of low-level communication libraries such as MPI. We present a technique to efficiently launch scripted applications on large-scale supercomputers using a hierarchical programming model.
This paper shows for the first time that distributed computing can be both reliable and efficient in an environment that is both highly dynamic and hostile. More specifically, we show how to maintain clusters of size $O(log N)$, each containing more than two thirds of honest nodes with high probability, within a system whose size can vary textit{polynomially} with respect to its initial size. Furthermore, the communication cost induced by each node arrival or departure is polylogarithmic with respect to $N$, the maximal size of the system. Our clustering can be achieved despite the presence of a Byzantine adversary controlling a fraction $bad leq {1}{3}-epsilon$ of the nodes, for some fixed constant $epsilon > 0$, independent of $N$. So far, such a clustering could only be performed for systems who size can vary constantly and it was not clear whether that was at all possible for polynomial variances.
It is known for some time that a random graph $G(n,p)$ contains w.h.p. a Hamiltonian cycle if $p$ is larger than the critical value $p_{crit}= (log n + log log n + omega_n)/n$. The determination of a concrete Hamiltonian cycle is even for values much larger than $p_{crit}$ a nontrivial task. In this paper we consider random graphs $G(n,p)$ with $p$ in $tilde{Omega}(1/sqrt{n})$, where $tilde{Omega}$ hides poly-logarithmic factors in $n$. For this range of $p$ we present a distributed algorithm ${cal A}_{HC}$ that finds w.h.p. a Hamiltonian cycle in $O(log n)$ rounds. The algorithm works in the synchronous model and uses messages of size $O(log n)$ and $O(log n)$ memory per node.
Distributed computing has become a common approach for large-scale computation of tasks due to benefits such as high reliability, scalability, computation speed, and costeffectiveness. However, distributed computing faces critical issues related to communication load and straggler effects. In particular, computing nodes need to exchange intermediate results with each other in order to calculate the final result, and this significantly increases communication overheads. Furthermore, a distributed computing network may include straggling nodes that run intermittently slower. This results in a longer overall time needed to execute the computation tasks, thereby limiting the performance of distributed computing. To address these issues, coded distributed computing (CDC), i.e., a combination of coding theoretic techniques and distributed computing, has been recently proposed as a promising solution. Coding theoretic techniques have proved effective in WiFi and cellular systems to deal with channel noise. Therefore, CDC may significantly reduce communication load, alleviate the effects of stragglers, provide fault-tolerance, privacy and security. In this survey, we first introduce the fundamentals of CDC, followed by basic CDC schemes. Then, we review and analyze a number of CDC approaches proposed to reduce the communication costs, mitigate the straggler effects, and guarantee privacy and security. Furthermore, we present and discuss applications of CDC in modern computer networks. Finally, we highlight important challenges and promising research directions related to CDC
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
