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The max-rain k-partition algorithm may be formulated as follows: Given a tree T with n edges and a nonnegative weight associated with each vertex, assign a cut to each of k distinct edges of T so as to maximize the weight of the lightest resulting connected subtree. An algorithm for this problem is presented which initially assigns all k cuts to one edge incident with a terminal vertex of T; thereafter the cuts are shifted from edge to adjacent edge on the basis of local information. An efficient implementation with complexity O(k 2. rd(T) + kn), where rd(T) is the number of edges in the radius of T, is described.An algorithm for a simpler problem, namely, the partitioning of Tinto the maximum number of connected components whose weight is bounded below, is then described. Combined with the technique of binary search, it yields an alternative algorithm for the max-rain k-partition problem with complexity dependent on the range of the given weights.

We compared and contrasted the maintainability of four open-source operating systems:Linux, FreeBSD, NetBSD, and OpenBSD. We used our categorization of common coupling in kernel-based software to highlight future maintenance problems. An unsafe definition is a definition of a global variable that can affect a kernel module if that definition is changed. For each operating system we determined a number of measures, including the number of global variables, the number of instances of global variables in the kernel and overall, as well as the number of unsafe definitions in the kernel and overall. We also computed the value of each our measures per kernel KLOC and per KLOC overall. For every measure and every ratio, Linux compared unfavorably to FreeBSD, NetBSD, and OpenBSD. Accordingly, we are concerned about the future maintainability of Linux.

One key to several quality factors of software is the way components are connected. Software coupling can be used to estimate a number of quality factors, including maintainability, complexity, and reliability. Object-oriented languages are designed to reduce the number of dependencies among classes, which encourages separation of concerns and should reduce the amount of coupling. At the same time, the objectoriented language features change the way the connections are made, how they must be analyzed, and how they are measured. This paper discusses software couplings based on object-oriented relationships between classes, specifically focusing on types of couplings that are not available until after the implementation is completed, and presents a static analysis tool that measures couplings among classes in Java packages. Data from evaluating the tool on several open-source projects are provided. The coupling measurement is based on source code, which has the advantage of being quantitative and more precise than previous measures, but the disadvantage of not being available before implementation, and thus not useful for some predictive efforts.