In this paper, we propose a family of graph partition similarity measures that take the topology of the graph into account. These graph-aware measures are alternatives to using set partition similarity measures that are not specifically designed for graphs. The two types of measures, graph-aware and set partition measures, are shown to have opposite behaviors with respect to resolution issues and provide complementary information necessary to compare graph partitions.

The probability that a complete binary prefix code has a self-synchronizing string approaches one, as the number of codewords tends to infinity.

In this paper we consider the problem of calculation of cell loss probabilities when M classes of stationary ON-OFF sources access a given multiplexer of large capacity. We show that when the number of sources of each type is large and scaled according to the capacity we can obtain an explicit analytic formula (O(1) in complexity) in terms of the parameters of the sources. This is based on a measure change technique combined with the use of uniform local limit theorems which gives estimates with a precise notion of the order of errors. We compare our results with standard Gaussian approximations which have been reported showing the improvement in the ATM context where cell loss probabilities are typically of the order 10/sup -9/.