External-Memory Network Analysis Algorithms for Naturally Sparse Graphs

In this paper, we present a number of network-analysis algorithms in the external-memory model. We focus on methods for large naturally sparse graphs, that is, n-vertex graphs that have O(n) edges and are structured so that this sparsity property holds for any subgraph of such a graph. We give efficient external-memory algorithms for the following problems for such graphs: - Finding an approximate d-degeneracy ordering; - Finding a cycle of length exactly c; - Enumerating all maximal cliques. Such problems are of interest, for example, in the analysis of social networks, where they are used to study network cohesion.Comment: 23 pages, 2 figures. To appear at the 19th Annual European Symposium on Algorithms (ESA 2011

Unlinkable Divisible Digital Cash without Trusted Third Party *

Abstract We present an efficient divisible digital cash scheme which is unlinkable and does not requireTrusted Third Party. The size of the coin is proportional to the size of the primes we use, i.e., hundreds of bytes. The computational and communication complexity of the protocol isproportional to a polynomial of the size of the primes and polylogarithm of the maximum number of pieces to which a coin can be subdivided. Keywords: digital cash, divisibility, unlinkability 1 Introduction Electronic cash has drawn much attention since it was introduced by Chaum [8]. Its basic ideais to provide an electronic payment scheme that ensures that the payer stays anonymous to the merchant during a transaction, yet the payer isn't able to cheat the merchant by spending false(forged) coins. Anonymity should also hold between a user and a bank (even though the bank issues thecoin, it shouldn't be able to determine which user a payment comes from, given the transcript of this payment). Additionally, in order to prevent the merchant from accepting a false coin,the scheme has to force the user to prove in a sound fashion that she uses a valid coin