The lattice dimension of a graph

We describe a polynomial time algorithm for, given an undirected graph G, finding the minimum dimension d such that G may be isometrically embedded into the d-dimensional integer lattice Z^d.Comment: 6 pages, 3 figure

A C++-embedded Domain-Specific Language for programming the MORA soft processor array

MORA is a novel platform for high-level FPGA programming of streaming vector and matrix operations, aimed at multimedia applications. It consists of soft array of pipelined low-complexity SIMD processors-in-memory (PIM). We present a Domain-Specific Language (DSL) for high-level programming of the MORA soft processor array. The DSL is embedded in C++, providing designers with a familiar language framework and the ability to compile designs using a standard compiler for functional testing before generating the FPGA bitstream using the MORA toolchain. The paper discusses the MORA-C++ DSL and the compilation route into the assembly for the MORA machine and provides examples to illustrate the programming model and performance

Optimal Universal Schedules for Discrete Broadcast

We study broadcast systems that distribute a series of data updates to a large number of passive clients. The updates are sent over a broadcast channel in the form of discrete packets. We assume that clients periodically access the channel to obtain the most recent update. Such scenarios arise in many practical applications, such as distribution of traffic information and market updates to mobile wireless devices

Mediatic graphs

Any medium can be represented as an isometric subgraph of the hypercube, with each token of the medium represented by a particular equivalence class of arcs of the subgraph. Such a representation, although useful, is not especially revealing of the structure of a particular medium. We propose an axiomatic definition of the concept of a `mediatic graph'. We prove that the graph of any medium is a mediatic graph. We also show that, for any non-necessarily finite set S, there exists a bijection from the collection M of all the media on a given set S (of states) onto the collection G of all the mediatic graphs on S.Comment: Four axioms replaced by two; two references added; Fig.6 correcte

Self-stabilizing TDMA Algorithms for Wireless Ad-hoc Networks without External Reference

Time division multiple access (TDMA) is a method for sharing communication media. In wireless communications, TDMA algorithms often divide the radio time into timeslots of uniform size, $\xi$, and then combine them into frames of uniform size, $\tau$. We consider TDMA algorithms that allocate at least one timeslot in every frame to every node. Given a maximal node degree, $\delta$, and no access to external references for collision detection, time or position, we consider the problem of collision-free self-stabilizing TDMA algorithms that use constant frame size. We demonstrate that this problem has no solution when the frame size is $\tau < \max\{2\delta,\chi_2\}$, where $\chi_2$ is the chromatic number for distance-$2$ vertex coloring. As a complement to this lower bound, we focus on proving the existence of collision-free self-stabilizing TDMA algorithms that use constant frame size of $\tau$. We consider basic settings (no hardware support for collision detection and no prior clock synchronization), and the collision of concurrent transmissions from transmitters that are at most two hops apart. In the context of self-stabilizing systems that have no external reference, we are the first to study this problem (to the best of our knowledge), and use simulations to show convergence even with computation time uncertainties