On cost-effective communication network designing

How to efficiently design a communication network is a paramount task for network designing and engineering. It is, however, not a single objective optimization process as perceived by most previous researches, i.e., to maximize its transmission capacity, but a multi-objective optimization process, with lowering its cost to be another important objective. These two objectives are often contradictive in that optimizing one objective may deteriorate the other. After a deep investigation of the impact that network topology, node capability scheme and routing algorithm as well as their interplays have on the two objectives, this letter presents a systematic approach to achieve a cost-effective design by carefully choosing the three designing aspects. Only when routing algorithm and node capability scheme are elegantly chosen can BA-like scale-free networks have the potential of achieving good tradeoff between the two objectives. Random networks, on the other hand, have the built-in character for a cost-effective design, especially when other aspects cannot be determined beforehand.Comment: 6 pages, 4 figure

Automorphisms of finite order on Gorenstein del Pezzo surfaces

In this note we shall determine all actions of groups of prime order p with p > 3 on Gorenstein del Pezzo (singular) surfaces Y of Picard number 1. We show that every order-p element in Aut(Y) (= Aut(Y'), Y' being the minimal resolution of Y) is lifted from a projective transformation of the projective plane. We also determine when Aut(Y) is finite in terms of the self intersection of the canonical divisor of Y, Sing(Y) and the number of singular members in the anti-canonical linear system of Y. In particular, we show that either |Aut(Y)| = 2^a 3^b for some 0 3 there is at least one element g_p of order p in Aut(Y) (hence |Aut(Y)| is infinite).Comment: 18 pages, Transactions of the American Mathematical Society, to appea