This demo will present both real and mocked-up usecases of a software application that enables accurate probabilistic modeling of new IP based services and their impact on network resources. The demonstration should be of general interest to Network Service Providers (NSP), device manufacturers, and application developers. Network planning and service analysis is a very important issue for today’s NSP’s; new communications devices and services emerge quickly (e.g., VoIP, Peer-to-peer filesharing, etc.) and end-users demand network resources that are up to the task. For the analyst, our tool leverages familiar UML style views, used to capture prototypical service “sessions”. It then allows annotation of the service model with a rich grammar, model conversion into semi-Markov form, and algorithm execution for network resource usage estimation. Ultimately, analysts gain insight into the impact of new consumer devices and services on their networks.

It is not known if planar integer linear programming is P-complete or if it is in NC, and the same can be said about the computation of the remainder sequence of the Euclidean algorithm applied to two integers. However, both computations are NC equivalent. The latter computational problem was reduced in NC to the former one by Deng [Mathematical Programming: Complexity and Application, Ph.D. dissertation, Stanford University, Stanford, CA, 1989; Proc. ACM Symp. on Parallel Algorithms and Architectures, 1989,pp. 110--116]. We now prove the converse NC-reduction.

We show NC-reduction of integer linear programming with two variables to the evaluation of the remainder sequence arising in the application of the Euclidean algorithm to two positive integers. Due to the previous result of X. Deng (1989), this implies NC-equivalence of both of these problems, whose membership in NC, as well as P-completeness, remain unresolved open problems.>

In recent years many advances have been made in solution techniques for specially structured 0–1 integer programming problems. In contrast, very little progress has been made on solving general (mixed) integer problems. This, of course, is not true when viewed from the theoretical side: H. W. Lenstra (1983) made a major breakthrough, obtaining a polynomial-time algorithm when the number of integer variables is fixed. We discuss a practical implementation of a Lenstra-like algorithm, based on the generalized basis reduction method of L. Lovász and H. E. Scarf (1988). This method allows us to avoid the ellipsoidal approximations required in Lenstra's algorithm. We report on the solution of a number of small (but difficult) examples, with up to 100 integer variables. Our computer code uses the linear programming optimizer CP LEX as a subroutine to solve the linear programming problems that arise. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.