Arif M. Khan

Multithreaded Algorithms for Maximum Matching in Bipartite Graphs

We design, implement, and evaluate algorithms for computing a matching of maximum cardinality in a bipartite graph on multicore and massively multithreaded computers. As computers with larger numbers of slower cores dominate the commodity processor market, the design of multithreaded algorithms to solve large matching problems becomes a necessity. Recent work on serial algorithms for the matching problem has shown that their performance is sensitive to the order in which the vertices are processed for matching. In a multithreaded environment, imposing a serial order in which vertices are considered for matching would lead to loss of concurrency and performance. But this raises the question: {\em Would parallel matching algorithms on multithreaded machines improve performance over a serial algorithm?}We answer this question in the affirmative. We report efficient multithreaded implementations of three classes of algorithms based on their manner of searching for augmenting paths: breadth-first-search, depth-first-search, and a combination of both. The Karp-Sipser initialization algorithm is used to make the parallel algorithms practical. We report extensive results and insights using three shared-memory platforms (a 48-core AMD Opteron, a 32-coreIntel Nehalem, and a 128-processor Cray XMT) on a representative set of real-world and synthetic graphs. To the best of our knowledge, this is the first study of augmentation-based parallel algorithms for bipartite cardinality matching that demonstrates good speedups on multithreaded shared memory multiprocessors.

A multithreaded algorithm for network alignment via approximate matching

Network alignment is an optimization problem to find the best one-to-one map between the vertices of a pair of graphs that overlaps as many edges as possible. It is a relaxation of the graph isomorphism problem and is closely related to the subgraph isomorphism problem. The best current approaches are entirely heuristic and iterative in nature. They generate real-valued heuristic weights that must be rounded to find integer solutions. This rounding requires solving a bipartite maximum weight matching problem at each iteration in order to avoid missing high quality solutions. We investigate substituting a parallel, half-approximation for maximum weight matching instead of an exact computation. Our experiments show that the resulting difference in solution quality is negligible. We demonstrate almost a 20-fold speedup using 40 threads on an 8 processor Intel Xeon E7-8870 system and now solve real-world problems in 36 seconds instead of 10 minutes.

Classifying Immunophenotypes With Templates From Flow Cytometry

We describe an algorithm to dynamically classify flow cytometry data samples into several classes based on their immunophenotypes. Flow cytometry data consists of fluorescence measurements of several proteins that characterize different cell types in blood or cultured cell lines. Each sample is initially clustered to identify the cell populations present in it. Using a combinatorial dissimilarity measure between cell populations in samples, we compute meta-clusters that correspond to the same cell population across samples. The collection of meta-clusters in a class of samples then describes a template for that class. We organize the samples into a template tree, and use it to classify new samples into existing classes or create a new class if needed. We dynamically update the templates and their statistical parameters as new samples are classified, so that the new information is reflected in the classes. We use our dynamic classification algorithm to classify T cells that on stimulation with an antibody show increased abundance of the proteins SLP-76 and ZAP-70. These proteins are involved in a platform that assembles signaling proteins in the immune response. We also use the algorithm to show that variation in an immune subsystem between individuals is a larger effect than variation in multiple samples from one individual.

Codesign Lessons Learned from Implementing Graph Matching on Multithreaded Architectures

Executing irregular, data-intensive workloads on multithreaded architectures can result in performance losses and scalability problems. Codesigning algorithms and architectures can realize high performance on irregular applications. A codesign study reveals four key lessons learned from implementing matching algorithms on various platforms.

Designing scalable b -M atching algorithms on distributed memory multiprocessors by approximation

A b-MATCHING is a subset of edges M such that at most b(v) edges in M are incident on each vertex v, where b(v) is specified. We present a distributed-memory parallel algorithm, b-SUITOR, that computes a b-MATCHING with more than half the maximum weight in a graph with weights on the edges. The approximation algorithm is designed to have high concurrency and low time complexity. We organize the implementation of the algorithm in terms of asynchronous supersteps that combine computation and communication, and balance the computational work and frequency of communication to obtain high performance. Since the performance of the b-SUITOR algorithm is strongly influenced by communication, we present several strategies to reduce the communication volume. We implement the algorithm using a hybrid strategy where inter-node communication uses MPI and intra-node computation is done with OpenMP threads. We demonstrate strong and weak scaling of b-SUITOR up to 16K processors on two supercomputers at NERSC. We compute a b-MATCHING in a graph with 2 billion edges in under 4 seconds using 16K processors.

New Approximation Algorithms for Minimum Weighted Edge Cover

We describe two new 3/2-approximation algorithms and a new 2-approximation algorithm for the minimum weight edge cover problem in graphs. We show that one of the 3/2-approximation algorithms, the Dual Cover algorithm, computes the lowest weight edge cover relative to previously known algorithms as well as the new algorithms reported here. The Dual Cover algorithm can also be implemented to be faster than the other 3/2-approximation algorithms on serial computers. Many of these algorithms can be extended to solve the b-Edge Cover problem as well. We show the relation of these algorithms to the K-Nearest Neighbor graph construction in semi-supervised learning and other applications.