We consider scheduling on a single machine with one non-availability period to minimize the weighted sum of completion times. We provide a preemptive algorithm with an approximation ratio arbitrarily close to the Golden Ratio, (1+ √ 5)/2+ε, which improves on a previously best known 2approximation. The non-preemptive version of the same algorithm yields a (2 + ε)-approximation.

In this paper we investigate similar triangles which are not congruent but have two pair congruent sides. We show that greatest lower bound of values for similarity ratio of such triangles is golden ratio. For right triangles, we prove that the supremum of values for similarity ratio is the square root of the golden ratio.

We present a series of results regarding conceptually simple algorithms for bipartite matching in various online and related models. We first consider a deterministic adversarial model. The best approximation ratio possible for a one-pass deterministic online algorithm is 1/2, which is achieved by any greedy algorithm. Dürr et al. [20] recently presented a 2-pass algorithm called Category-Advic...

Mario Livio is a scientist and self−proclaimed "art fanatic" who owns many hundreds of art books. Recently, he combined his passions for science and art in two popular books, The Accelerating Universe, which appeared in 2000, and The Golden Ratio, reviewed in this issue of Plus. The former book discusses "beauty" as an essential ingredient in fundamental theories of the universe. The latter dis...

In this paper we propose a new data declustering scheme for range queries. Our scheme is based on Golden Ratio Sequences (GRS), which have found applications in broadcast disks, hashing, packet routing, etc. We show by analysis and simulation that GRS is nearly the best possible scheme for 2-dimensional range queries. Speciically, it is the best possible scheme when the number of disks (M) is a...

MATERIAL AND METHODS

There are useful and useless golden ratios. The one helps in traffic. rather mysterious arises hydrodynamics of point vortices, which we discuss detail.