Abstract-The rapidly increasing energy consumption by computing and communications equipment is a significant economic and environmental problem that needs to be addressed. Ethernet network interface controllers (NICs) in the US alone consume hundreds of millions of US dollars in electricity per year. Most Ethernet links are underutilized and link energy consumption can be reduced by operating at a lower data rate. In this paper, we investigate Adaptive Link Rate (ALR) as a means of reducing the energy consumption of a typical Ethernet link by adaptively varying the link data rate in response to utilization. Policies to determine when to change the link data rate are studied. Simple policies that use output buffer queue length thresholds and fine-grain utilization monitoring are shown to be effective. A Markov model of a state-dependent service rate queue with rate transitions only at service completion is used to evaluate the performance of ALR with respect to the mean packet delay, the time spent in an energy-saving low link data rate, and the oscillation of link data rates. Simulation experiments using actual and synthetic traffic traces show that an Ethernet link with ALR can operate at a lower data rate for over 80 percent of the time, yielding significant energy savings with only a very small increase in packet delay.

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We consider the following randomized algorithm for finding a matching M in an arbitrary graph G = (V, E ) . Repeatedly, choose a random vertex u , then a random neighbour u of u . Add edge { u , u ) to M and delete vertices u, u from G along with any vertices that become isolated. Our main result is that there exists a positive constant E such that the expected ratio of the size of the matching produced to the size of largest matching in G is at least 0.5 + e. We obtain stronger results for sparse graphs and trees and consider extensions to hypergraphs. 0 1995 John Wiley & Sons, Inc.

Let P be a graph property which is preserved by removal of edges. A random maximal P-graph is obtained from n independent vertices by randomly adding edges, at each stage choosing uniformly among edges whose inclusion would not destroy property P, until no further edges can be added. We address the question of the number of edges of a random maximal P-graph for several properties P, in particular the cases of "bipartite" and "triangle-free.'' A variety of techniques are used to show that the size of the random maximal bipartite graph is quadratic in n but of order only n3" in the triangle-free case. Along the way we obtain a slight improvement in the lower bound of the Ramsey number r(3, t).

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