Space Efficient Algorithms for Breadth-Depth Search

Continuing the recent trend, in this article we design several space-efficient algorithms for two well-known graph search methods. Both these search methods share the same name {\it breadth-depth search} (henceforth {\sf BDS}), although they work entirely in different fashion. The classical implementation for these graph search methods takes $O(m+n)$ time and $O(n \lg n)$ bits of space in the standard word RAM model (with word size being $\Theta(\lg n)$ bits), where $m$ and $n$ denotes the number of edges and vertices of the input graph respectively. Our goal here is to beat the space bound of the classical implementations, and design $o(n \lg n)$ space algorithms for these search methods by paying little to no penalty in the running time. Note that our space bounds (i.e., with $o(n \lg n)$ bits of space) do not even allow us to explicitly store the required information to implement the classical algorithms, yet our algorithms visits and reports all the vertices of the input graph in correct order.Comment: 12 pages, This work will appear in FCT 201

Theoretically Efficient Parallel Graph Algorithms Can Be Fast and Scalable

There has been significant recent interest in parallel graph processing due to the need to quickly analyze the large graphs available today. Many graph codes have been designed for distributed memory or external memory. However, today even the largest publicly-available real-world graph (the Hyperlink Web graph with over 3.5 billion vertices and 128 billion edges) can fit in the memory of a single commodity multicore server. Nevertheless, most experimental work in the literature report results on much smaller graphs, and the ones for the Hyperlink graph use distributed or external memory. Therefore, it is natural to ask whether we can efficiently solve a broad class of graph problems on this graph in memory. This paper shows that theoretically-efficient parallel graph algorithms can scale to the largest publicly-available graphs using a single machine with a terabyte of RAM, processing them in minutes. We give implementations of theoretically-efficient parallel algorithms for 20 important graph problems. We also present the optimizations and techniques that we used in our implementations, which were crucial in enabling us to process these large graphs quickly. We show that the running times of our implementations outperform existing state-of-the-art implementations on the largest real-world graphs. For many of the problems that we consider, this is the first time they have been solved on graphs at this scale. We have made the implementations developed in this work publicly-available as the Graph-Based Benchmark Suite (GBBS).Comment: This is the full version of the paper appearing in the ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), 201

Correct and Efficient Antichain Algorithms for Refinement Checking

The notion of refinement plays an important role in software engineering. It is the basis of a stepwise development methodology in which the correctness of a system can be established by proving, or computing, that a system refines its specification. Wang et al. describe algorithms based on antichains for efficiently deciding trace refinement, stable failures refinement and failures-divergences refinement. We identify several issues pertaining to the soundness and performance in these algorithms and propose new, correct, antichain-based algorithms. Using a number of experiments we show that our algorithms outperform the original ones in terms of running time and memory usage. Furthermore, we show that additional run time improvements can be obtained by applying divergence-preserving branching bisimulation minimisation

HybridMiner: Mining Maximal Frequent Itemsets Using Hybrid Database Representation Approach

In this paper we present a novel hybrid (arraybased layout and vertical bitmap layout) database representation approach for mining complete Maximal Frequent Itemset (MFI) on sparse and large datasets. Our work is novel in terms of scalability, item search order and two horizontal and vertical projection techniques. We also present a maximal algorithm using this hybrid database representation approach. Different experimental results on real and sparse benchmark datasets show that our approach is better than previous state of art maximal algorithms.Comment: 8 Pages In the proceedings of 9th IEEE-INMIC 2005, Karachi, Pakistan, 200

Platform Dependent Verification: On Engineering Verification Tools for 21st Century

The paper overviews recent developments in platform-dependent explicit-state LTL model checking.Comment: In Proceedings PDMC 2011, arXiv:1111.006