The multiplication of large spare matrices is a basic operation in many scientific and engineering applications. There exist some high-performance library routines for this operation. They are often optimized based on the target architecture. For a parallel environment, it is essential to partition the entire operation into well balanced tasks and assign them to individual processing elements. Most of the existing techniques partition the given matrices based on some kind of workload estimation. For irregular sparse matrices on PC clusters, however, the workloads may not be well estimated in advance. Any approach other than run-time dynamic partitioning may degrade performance. In this paper, we apply our super-programming approach to parallel large matrix multiplication on PC clusters. In our approach, tasks are partitioned into super-instructions that are dynamically assigned to member computer nodes. Thus, the load balancing logic is separated from the computing logic; the former is taken over by the runtime environment. Our super-programming approach facilitates ease of program development and targets high efficiency in dynamic load balancing. Workloads can be balanced effectively and the optimization overhead is small. The results prove the viability of our approach.

We introduce PC Linux cluster computing techniques to an Evolutionary Graph Generation (EGG) system, and successfully implement the parallel version of the EGG system, called PEGG. Our survey satisfactorily shows that the parallel evolutionary approach meets our expectation that the final solutions obtained from PEGG will be as good as or better than those obtained from EGG, and that PEGG can ultimately improve the speed of evolution.

We developed a PC cluster system which consists of 100 PCs as a test bed for massively parallel query processing. Each PC employs the 200 MHz Pentium Pro CPU and is connected with others through an ATM switch. Because the query processing applications are insensitive to the communication latency and mainly perform integer operations, the ATM connected PC cluster approach can be considered a reasonable solution for high performance database servers with low costs. However, there has been no challenge to construct large scale PC clusters for database applications, as far as the authors know. Though we employed commodity components as much as possible, we developed the DBMS itself, because that was a key component for obtaining high performance in parallel query processing, and there seemed no system which could meet our demand. On each PC node, a server program which acts as a database kernel is running to process the queries in cooperation with other nodes. The kernel was designed to execute pipelined operators and handle voluminous data efficiently, to achieve high performance on complex decision support type queries. We used the standard benchmark, TPC-D, on a 100 GB database to verify the feasibility of our approach, through comparison of our system with commercial parallel systems. As a whole, our system exhibited sufficiently high performance which was competitive with the current TPC-D top records, in spite of not using indices. For some heavy queries in the benchmark, which have high selectivity and joinability, our system performed much better. In addition, we applied transposed file organization to the database for further performance improvement. The transposed file organization vertically partitions the tuples, enabling attribute-by-attribute access to the relations. This resulted in significant performance improvement by reducing the amount of disk I/O and shifting the bottleneck to computation.