A Note on the Critical Problem for Matroids

Let M be a matroid representable over GF(q) and S be a subset of its ground set. In this note we prove that S is maximal with the property that the critical exponent c(M|S; q) does not exceed k if and only if S is maximal with the property that c(M · S) ≤ k. In addition, we show that, for regular matroids, the corresponding result holds for the chromatic number. © 1984, Academic Press Inc. (London) Limited. All rights reserved

Algorithms for Multicommodity Flows in Planar Graphs

This paper gives efficient algorithms for the multicommodity flow problem for two classes Ct2 and Co~ of planar undirected graphs. Every graph in Ct2 has two face boundaries B t and B 2 such that each of the source-sink pairs lies on B 1 or B 2. On the other hand, every graph in Cot has a face boundary B t such that some of the source-sink pairs lie on B 1 and all the other pairs share a common sink lying on B t. The algorithms run in O(kn + nT(n)) time if a graph has n vertices and k source-sink pairs and T(n) is the time required for finding the single-source shortest paths in a planar graph of n vertices

A linear algorithm for finding Hamiltonian cycles in 4-connected maximal planar graphs

AbstractThis paper describes a linear time algorithm to find a Hamiltonian cycle in an arbitrary 4-connected maximal planar graph. The algorithm is based on our simplified version of Whitney's proof of his theorem: every 4-connected maximal planar graph has a Hamiltonian cycle

TMS320C3X User's Guide", Texas Instruments

In this paper we present our ongoing research about the integration of ubiquitous computing systems into classroom settings, in order to give basic support for some classroom and field activities. We have developed some web application components using Java technology and configured a classroom with wireless network access and a web camera for our purposes. In this classroom the students interact between them and with the professor through an Internet enabled PDA, using the different modules described in this paper. We include our evaluations about the performance and usability of the system in a computer science related course of the University of Tokushima and the future research and development work 1