1,913 research outputs found
Computation of Poincare-Betti series for monomial rings
The multigraded Poincare-Betti series P_R^k(x_1,...,x_n; t) of a monomial
ring k[x_1,...,x_n]/ on a finite number of monomial generators has the form
(1+tx_1)(1+tx_2)...(1+tx_n)/b_(R,k)(x_1,...,x_n; t), where
b_(R,k)(x_1,...,x_n;t) is a polynomial depending only on the monomial set M and
the characteristic of the field k. I present a computer program designed to
calculate the polynomial b_(R,k) for a given field characteristic and a given
set of monomial generators.Comment: 8 pages, prepared for the School and Workshop on Algebraic geometry
and statistics at Politecnico Torino in September 200
Cautious Weight Tuning for Link State Routing Protocols
Link state routing protocols are widely used for intradomain routing in the Internet. These protocols are simple to administer and automatically update paths between sources and destinations when the topology changes. However, finding link weights that optimize network performance for a given traffic scenario is computationally hard. The situation is even more complex when the traffic is uncertain or time-varying. We present an efficient heuristic for finding link settings that give uniformly good performance also under large changes in the traffic. The heuristic combines efficient search techniques with a novel objective function. The objective function combines network performance with a cost of deviating from desirable features of robust link weight settings. Furthermore, we discuss why link weight optimization is insensitive to errors in estimated traffic data from link load measurements. We assess performance of our method using traffic data from an operational IP backbone
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