One-way, dataflow constraints are commonly used in graphical interface toolkits, programming environments, and circuit applications. Previous papers on dataflow constraints have focused on the design and implementation of individual algorithms. In contrast, this article focuses on the lessons we have learned from a decade of implementing competing algorithms in the Garnet and Amulet graphical interface toolkits. These lessons reveal the design and implementation tradeoffs for different one-way, constraint satisfaction algorithms. The most important lessons we have learned are that (1) mark-sweep algorithms are more efficient than topological ordering algorithms; (2) lazy and eager evaluators deliver roughly comparable performance for most applications; and (3) constraint satisfaction algorithms have more than adequate speed, except that the storage required by these algorithms can be problematic.

In applications such as landscape ecology, computer mod eling is used to assess habitat fragmentation and its ecological implications. Maps (two-dimensional grids) of habitat clusters or patches are analyzed to determine the number, location, and sizes of clusters. Recently, improved sequential and parallel implementations of the Hoshen- Kopelman cluster identification algorithm have been designed. These implementations use a finite state ma chine to reduce redundant integer comparisons during the cluster identification process. The sequential implementa tion for large maps performs cluster identification by par titioning the map along row boundaries and merging the results of the partitions. The parallel implementation on a 32-processor Thinking Machines CM-5 provides an effi cient mechanism for performing cluster identification in parallel. Although the sequential implementation achieved promising speed improvements ranging from 1.39 to 2.00 over an existing Hoshen-Kopelman implementation, the parallel implementation achieved a minimum speedup of 5.41 over the improved sequential implementation, exe cuted on a Sun SPARCstation 10.

One-way constraints have been widely incorporated in research toolkits for constructing graphical applications. However, although a number of studies have examined the performance of these toolkits' constraint satisfaction algorithms, there have not been any empirical studies that have examined how programmers use constraints in actual applications. This paper reports the results of a study intended to address these matters. Seven graphical applications were chosen for their diversity and profiling information was gathered about their use of constraints, The data reveal that constraint networks tend to be modular, that is, divided into a number c~fsmall, independent sets of constraints rather than one mono] ithic set of constraints. This finding suggests that constraint satisfaction algorithms should be able to resatisfy constraints rapidly after a change to one or more variables. It also suggests that debugging constraints should not be unduly burdensome on a programmer since the number of constraints that must be examined to find the source of an error is not terriblly large. Overall, the results of this study should provide a repository of data that will be useful in directing future research on optimizing constraint solvers and developing effective debugging techniques.

RAID-6 codes protect disk array storage systems from two-disk failures. This article presents a complete treatment of a class of RAID-6 codes, called minimum density RAID-6 codes, that have an optimal blend of performance properties. There are two families of minimal density RAID-6 codes: Blaum-Roth codes and Liberation codes, and a separate special-purpose code called the Liber8tion code. The first of these have been known since the late 1990's, while the latter two are new constructions. In this article, we motivate, demonstrate, and evaluate the minimum density codes, comparing them to EVENODD and RDP codes, which represent the state-of-the-art in RAID-6. Following that, we prove that the codes indeed fit the RAID-6 methodology, and cite their implementation in an open-source library.

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