Competitive randomized algorithms for nonuniform problems

Competitive analysis is concerned with comparing the performance of on-line algorithms with that of optimal off-line algorithms. In some cases randomization can lead to algorithms with improved performance ratios on worst-case sequences. In this paper we present new randomized on-line algorithms for snoopy caching and the spin-block problem. These algorithms achieve competitive ratios approachinge/(e–1) 1.58 against an oblivious adversary. These ratios are optimal and are a surprising improvement over the best possible ratio in the deterministic case, which is 2. We also consider the situation when the request sequences for these problems are generated according to an unknown probability distribution. In this case we show that deterministic algorithms that adapt to the observed request statistics also have competitive factors approachinge/(e–1). Finally, we obtain randomized algorithms for the 2-server problem on a class of isosceles triangles. These algorithms are optimal against an oblivious adversary and have competitive ratios that approache/(e–1). This compares with the ratio of 3/2 that can be achieved on an equilateral triangle.Supported in part by the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS), an NSF Science and Technology Center funded under NSF Contract STC-88-09648 and supported by the New Jersey Commission on Science and Technology.     

Entrapment of water by subunit c of ATP synthase.

We consider an ancient protein, and water as a smooth surface, and show that the interaction of the two allows the protein to change its hydrogen bonding to encapsulate the water. This property could have made a three-dimensional microenvironment, 3-4 Gyr ago, for the evolution of subsequent complex water-based chemistry. Proteolipid, subunit c of ATP synthase, when presented with a water surface, changes its hydrogen bonding from an alpha-helix to beta-sheet-like configuration and moves away from its previous association with lipid to interact with water surface molecules. Protein sheets with an intra-sheet backbone spacing of 3.7A and inter-sheet spacing of 6.0 A hydrogen bond into long ribbons or continuous surfaces to completely encapsulate a water droplet. The resulting morphology is a spherical vesicle or a hexagonal crystal of water ice, encased by a skin of subunit c. Electron diffraction shows the crystals to be highly ordered and compressed and the protein skin to resemble beta-sheets. The protein skin can retain the entrapped water over a temperature rise from 123 to 223 K at 1 x 10(-4) Pa, whereas free water starts to sublime significantly at 153 K.     

A strongly competitive randomized paging algorithm

Thepaging problem is that of deciding which pages to keep in a memory ofk pages in order to minimize the number of page faults. We develop thepartitioning algorithm, a randomized on-line algorithm for the paging problem. We prove that its expected cost on any sequence of requests is within a factor ofH _k of optimum. (H _k is thekth harmonic number, which is about ln(k).) No on-line algorithm can perform better by this measure. Our result improves by a factor of two the best previous algorithm.     

The published DNA sequence of human cytomegalovirus strain AD169 lacks 929 base pairs affecting genes UL42 and UL43

Compared with the published DNA sequence (M. S. Chee, et al. Curr. Top. Microbiol. Immunol. 154:125-170, 1990), most isolates of human cytomegalovirus strain AD169 contain an additional 929 bp after nucleotide 54612. This results in a changed reading frame for the 5'-terminal 50 codons of gene UL42 and expansion of gene UL43 (a US22 family member) from 187 (3'-truncated) to 423 (full-length) codons. The UL42 and UL43 gene products are nonessential for growth in culture.     

All-pairs shortest paths and the essential subgraph

The essential subgraph H of a weighted graph or digraphG contains an edge (v, w) if that edge is uniquely the least-cost path between its vertices. Let s denote the number of edges ofH. This paper presents an algorithm for solving all-pairs shortest paths onG that requires O(ns+n² logn) worst-case running time. In general the time is equivalent to that of solvingn single-source problems using only edges inH. For general models of random graphs and digraphsG, s=0(n logn) almost surely. The subgraphH is optimal in the sense that it is the smallest subgraph sufficient for solving shortest-path problems inG. Lower bounds on the largest-cost edge ofH and on the diameter ofH andG are obtained for general randomly weighted graphs. Experimental results produce some new conjectures about essential subgraphs and distances in graphs with uniform edge costs.Much of this research was carried out while the author was a Visiting Fellow at the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS).     

Radio-frequency-preionized xenon z-pinch source for extreme ultraviolet lithography

Intense amplified spontaneous emission is generated in generally axial directions in a recombining uniform Z pinch. This effect allows the generation of highly efficient soft x-ray beams, including the intense xenon-band emission at 134 ?, of interest for extreme ultraviolet lithography. We discuss the characteristics of this source, including optimization of the xenon-helium mix and measurements of source size, brightness, and positional and amplitude stability. The issues involved in increasing power to the lithography class by an increase in the repetition rate are discussed. The life and operating costs of a lithography source are considered.     

A strongly competitive randomized paging algorithm

Thepaging problem is that of deciding which pages to keep in a memory ofk pages in order to minimize the number of page faults. We develop thepartitioning algorithm, a randomized on-line algorithm for the paging problem. We prove that its expected cost on any sequence of requests is within a factor ofH _k of optimum. (H _k is thekth harmonic number, which is about ln(k).) No on-line algorithm can perform better by this measure. Our result improves by a factor of two the best previous algorithm.Partial support for D. D. Sleator was provided by DARPA, ARPA Order 4976, Amendment 20, monitored by the Air Force Avionics Laboratory under Contract F33615-87-C-1499, and by the National Science Foundation under Grant CCR-8658139.     

Optimum second-harmonic generation in lithium niobate

An experimental study of noncritically phase-matched (theta_{m} = 90deg) second-harmonic generation is described, in which the theoretical predictions of Boyd and Kleinman with regard to strength of focusing and effect of mismatch are closely verified. Radiation at 1.084 μ from a He-Ne laser was employed to generate light at 542 nm in LiNbO3.