On Colorings of Maps

A fixed-point free map f : X ! X is said to be colorable with k colors if there exists a closed cover C of X consisting of k elements such that C " f(C) = ; for every C in C. It is shown that every fixed-point free continuous selfmap of a compact space X with dim X n can be colored with n + 3 colors. Similar results are obtained for finitely many maps. It is shown that every free Z p -action on an n-dimensional compact space X has genus at most n + 1

Hierarchical resource allocation for robust in-home video streaming

High quality video streaming puts high demands on network and processor resources. The bandwidth of the communication medium and the timely arrival of the frames necessitate a tight resource allocation. Given the dynamic environment where videos are started and stopped and electro-magnetic perturbations affect the bandwidth of the wireless medium, a framework is needed that reacts timely to the changes in network load and network operational conditions. This paper describes a hierarchical framework, which can handle the dynamic network resource allocation in a timely manner