Decomposition of Trees and Paths via Correlation

We study the problem of decomposing (clustering) a tree with respect to costs attributed to pairs of nodes, so as to minimize the sum of costs for those pairs of nodes that are in the same component (cluster). For the general case and for the special case of the tree being a star, we show that the problem is NP-hard. For the special case of the tree being a path, this problem is known to be polynomial time solvable. We characterize several classes of facets of the combinatorial polytope associated with a formulation of this clustering problem in terms of lifted multicuts. In particular, our results yield a complete totally dual integral (TDI) description of the lifted multicut polytope for paths, which establishes a connection to the combinatorial properties of alternative formulations such as set partitioning.Comment: v2 is a complete revisio

Computer-aided programming for multiprocessing systems

As both the number of processors and the complexity of problems to be solved increase, programming multiprocessing systems becomes more difficult and error-prone. This report discusses parallel models of computation and tools for computer-aided programming (CAP). Program development tools are necessary since programmers are not able to develop complex parallel programs efficiently. In particular, a CAP tool, named Hypertool, is described here. It performs scheduling and handles the communication primitive insertion automatically so that many errors are eliminated. It also generates the performance estimates and other program quality measures to help programmers in improving their algorithms and programs. Experiments have shown that up to a 300% performance improvement can be achieved by computer-aided programming

Recent Advances in Graph Partitioning

We survey recent trends in practical algorithms for balanced graph partitioning together with applications and future research directions