Several approaches to finding the connected components of a graph on a hypercube multicomputer are proposed and analyzed. The results of experiments conducted on an NCUBE hypercube are also presented. The experimental results support the analysis.

As software is getting more valuable, unauthorized users or malicious programmers illegally copies and distributes copyrighted software over online service provider (OSP) and P2P networks. To detect, block, and remove pirated software (illegal programs) on OSP and P2P networks, this paper proposes a new filtering approach using software birthmark, which is unique characteristics of program and can be used to identify each program. Software birthmark typically includes constant values, library information, sequence of function calls, and call graphs, etc. We target Microsoft Windows applications and utilize the numbers and names of DLLs and APIs stored in a Windows executable file. Using that information and each cryptographic hash value of the API sequence of programs, we construct software birthmark database. Whenever a program is uploaded or downloaded on OSP and P2P networks, we can identify the program by comparing software birthmark of the program with birthmarks in the database. It is possible to grasp to some extent whether software is an illegally copied one. The experiments show that the proposed software birthmark can effectively identify Windows applications. That is, our proposed technique can be employed to efficiently detect and block pirated programs on OSP and P2P networks.

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We describe two hypercube algorithms to find the biconnected components (i.e., blocks) of a connected undirected graph. One is a modified version of the Tarjan-Vishkin algorithm. The two hypercube algorithms were experimentally evaluated on an NCUBE/7 MIMD hypercube computer. The two algorithms have comparable performance and efficiencies as high as 0.7 were observed. Keywords and phrasesHypercube computing, MIMD computer, parallel programming, biconnected components __________________ * This research was supported in part by the National Science Foundation under grants DCR84-20935 and MIP 86-17374 1 2 INTRODUCTIONIn this paper we develop two biconnected component (i.e., block) algorithms suitable for medium grained MIMD hypercubes. The first algorithm is an adaptation of the algorithm of Tarjan and Vishkin [TARJ85]. Tarjan and Vishkin provide parallel CRCW and CREW PRAM implementations of their algorithm. The CRCW PRAM implementation of Tarjan and Vishkin runs in O(logn) time and uses O(n +m) processors. Here n and m are, respectively, the number of vertices and edges in the input connected graph. The CREW PRAM implementation runs in O(log 2 n) time using O(n 2 /log 2 n) processors.A PRAM algorithm that use p processors and t time can be simulated by a p processor hypercube in O(tlog 2 p) time using the random access read and write algorithms of Nassimi and Sahni [NASS81]. The CREW PRAM algorithm of [TARJ85] therefore results in an O(log 3 n) time O(n +m) processor hypercube algorithm. The CREW PRAM algorithm results in an O(log 4 n) time O(n 2 /log 2 n) processor hypercube algorithm. Using the results of Dekel, Nassimi, and Sahni [DEKE81] the biconnected components can be found in O(log 2 n) time using O(n 3 /logn) processors.The processor-time product of a parallel algorithm is a measure of the total amount of work done by the algorithm. For the three hypercube algorithms just mentioned, the processor-time product is, respectively, O(n 2 log 3 n) (assuming m ∼ ∼ O(n 2 )), O(n 2 log 2 n), and O(n 3 logn). In each case the processor-time product is larger than that for the single processor biconnected components algorithm (O(n 2 ) when m= O(n 2 )). As a result of this, we do not expect any of the above three hypercube algorithms to outperform the single processor algorithm unless the number of available processors, p, is sufficiently large. For example, if n = 1024, then the CRCW simulation on a hypercube does O(log 3 n) ∼ ∼1000 times more work than the uniprocessor algorithm. So we will need approximately 1000 processors just to break even.In fact, the processor-time product for many of the asymptotically fastest parallel hypercube algorithms exceeds that of the fastest uniprocessor algorithm by at least a multiplicative factor of log k n for some k, k≥1. As a result, the simulation of these algorithms on commercially available hypercubes with a limited number of processors does not yield good results. Consequently, there is often a wide disparity between the asymptotic algorithms developed for PRAM...