A multilevel algorithm for force-directed graph-drawing

We describe a heuristic method for drawing graphs which uses a multilevel framework combined with a force-directed placement algorithm. The multilevel technique matches and coalesces pairs of adjacent vertices to define a new graph and is repeated recursively to create a hierarchy of increasingly coarse graphs, G0, G1, …, GL. The coarsest graph, GL, is then given an initial layout and the layout is refined and extended to all the graphs starting with the coarsest and ending with the original. At each successive change of level, l, the initial layout for Gl is taken from its coarser and smaller child graph, Gl+1, and refined using force-directed placement. In this way the multilevel framework both accelerates and appears to give a more global quality to the drawing. The algorithm can compute both 2 & 3 dimensional layouts and we demonstrate it on examples ranging in size from 10 to 225,000 vertices. It is also very fast and can compute a 2D layout of a sparse graph in around 12 seconds for a 10,000 vertex graph to around 5-7 minutes for the largest graphs. This is an order of magnitude faster than recent implementations of force-directed placement algorithms.

Quality-of-context driven autonomicity

Optimisation in wireless sensor networks is necessary due to the resource constraints of individual devices, bandwidth limits of the communication channel, relatively high probably of sensor failure, and the requirement constraints of the deployed applications in potently highly volatile environments. This paper presents BioANS, a protocol designed to optimise a wireless sensor network for resource efficiency as well as to meet a requirement common to a whole class of WSN applications - namely that the sensor nodes are dynamically selected on some qualitative basis, for example the quality by which they can provide the required context information. The design of BioANS has been inspired by the communication mechanisms that have evolved in natural systems. The protocol tolerates randomness in its environment, including random message loss, and incorporates a non-deterministic ’delayed-bids’ mechanism. A simulation model is used to explore the protocol’s performance in a wide range of WSN configurations. Characteristics evaluated include tolerance to sensor node density and message loss, communication efficiency, and negotiation latency .