Fast reoptimization for the minimum spanning tree problem

AbstractWe study reoptimization versions of the minimum spanning tree problem. The reoptimization setting can generally be formulated as follows: given an instance of the problem for which we already know some optimal solution, and given some “small” perturbations on this instance, is it possible to compute a new (optimal or at least near-optimal) solution for the modified instance without ex nihilo computation? We focus on two kinds of modifications: node-insertions and node-deletions. When k new nodes are inserted together with their incident edges, we mainly propose a fast strategy with complexity O(kn) which provides a max{2,3−(2/(k−1))}-approximation ratio, in complete metric graphs and another one that is optimal with complexity O(nlogn). On the other hand, when k nodes are deleted, we devise a strategy which in O(n) achieves approximation ratio bounded above by 2⌈|Lmax|/2⌉ in complete metric graphs, where Lmax is the longest deleted path and |Lmax| is the number of its edges. For any of the approximation strategies, we also provide lower bounds on their approximation ratios

THE DESIGN OF KNOWLEDGE-BASED SYSTEMS FOR MANAGING ILL-STRUCTURED SOFTWARE PROJECTS

Current planning and control procedures for large-scale software projects are not sufficiently equipped to deal with changing or imprecise requirements, resource breakdowns, unexpected delays, etc. We propose a solution for managing change in projects, based on a semantic model of the software design and development processes. At the heart of this technique is the formation of islands of project knowledge in a way that facilitates dealing with most design and plan revisions locally. A protocol for interactive change management is presented that advocates need-based formation of coalitions between islands as a means for graceful degradation in the place of strict hierarchical control. The results of initial empirical investigations of the usability of the approach and plans for its continuing evaluation are also reported.Information Systems Working Papers Serie