Approximating 1-dimensional TSP Requires Omega(n log n) Comparisons

We give a short proof that any comparison-based n^(1-epsilon)-approximation algorithm for the 1-dimensional Traveling Salesman Problem (TSP) requires Omega(n log n) comparisons.Comment: Superseded by "On the complexity of approximating Euclidean traveling salesman tours and minimum spanning trees", by Das et al; Algorithmica 19:447-460 (1997

Nearly Linear-Work Algorithms for Mixed Packing/Covering and Facility-Location Linear Programs

We describe the first nearly linear-time approximation algorithms for explicitly given mixed packing/covering linear programs, and for (non-metric) fractional facility location. We also describe the first parallel algorithms requiring only near-linear total work and finishing in polylog time. The algorithms compute $(1+\epsilon)$-approximate solutions in time (and work) $O^*(N/\epsilon^2)$, where $N$ is the number of non-zeros in the constraint matrix. For facility location, $N$ is the number of eligible client/facility pairs

On-Line File Caching

In the on-line file-caching problem problem, the input is a sequence of requests for files, given on-line (one at a time). Each file has a non-negative size and a non-negative retrieval cost. The problem is to decide which files to keep in a fixed-size cache so as to minimize the sum of the retrieval costs for files that are not in the cache when requested. The problem arises in web caching by browsers and by proxies. This paper describes a natural generalization of LRU called Landlord and gives an analysis showing that it has an optimal performance guarantee (among deterministic on-line algorithms). The paper also gives an analysis of the algorithm in a so-called ``loosely'' competitive model, showing that on a ``typical'' cache size, either the performance guarantee is O(1) or the total retrieval cost is insignificant.Comment: ACM-SIAM Symposium on Discrete Algorithms (1998

A concept for universal pliers

By modification in existing design, pliers can be made to have one pair of handles that will accept number of different jaws. Concept is useful for light to medium duty service. Complete set of jaws may be made to suit specific hobbies or applications

Appropriations Redux: A Critical Look at the Fiscal Year 1988 Continuing Resolution

On January 25, 1988, in his State of the Union Address, President Reagan blasted Congress for the budget process culminating in the Fiscal Year 1988 (FY 88) continuing resolution. 1 Contending that [m]ost of you in this chamber didn\u27t know what was in this [2100-page] catch all bill and [accompanying conference] report, the President boldly proclaimed that he would not sign another one of these. 2 This damning statement, rather than inciting the hostility associated with unfounded accusations, provoked the wild appreciation associated with a minister preaching to the faithful. Indeed, since Congress\u27s passage of the resolution, pledges of support for the President\u27s stand have been made by enough Congressmen and Senators to sustain such a veto. 3 There is good reason to dislike the FY 88 continuing resolution: the bill shattered Congress\u27s reputation as a deliberative body. Fearing the imminent shutdown of the government, 4 Congress adopted internal rules to preclude debate and amendment and effectively to deny access to the final version of the bill. 5 In essence, the resolution appears the secretive work-product of powerful legislators and their aides. This article\u27s concern is the recent proliferation of continuing resolutions and the legal issues associated with that proliferation -- matters that received only scant attention in my earlier piece on limitation riders. 6 In reviewing the causes and contents of last year\u27s continuing resolution, this article will not altogether remove the negative cast put on continuing resolutions. 7 At the same time, ..

Discovery of an Attorney’s Work Product in Subsequent Litigation

During the last century, the industrialization of agriculture has led to changes in the landscape and many important habitats have disappeared. Habitat loss and fragmentation and an increased use of agrichemicals have led to biodiversity declines in the agricultural landscape. The negative impacts on pollinators, in particular, must be taken serious because they provide an important ecosystem service when they pollinate crops. Monitoring of pollinators is therefore important to examine the factors that affect pollination. The pan trap method is commonly used in the monitoring of pollinating insects, but few studies have evaluated the effect of trap color on the collection of different groups of pollinators. Pollinators were collected using the pan trap method with blue, yellow and white bowls to examine if there were difference in the attraction to traps of different colors among different groups of pollinators. Lepturine beetles (Lepturinae spp.), bee beetles (Trichius spp.) and the bumblebees (Bombus spp.) preferred the blue traps while rose chafers (Cetoniidae spp.) and hoverflies (Syrphidae spp.) preferred the yellow traps. Hence pan traps of different colors may be specific for different groups of pollinators

A Bound on the Sum of Weighted Pairwise Distances of Points Constrained to Balls

We consider the problem of choosing Euclidean points to maximize the sum of their weighted pairwise distances, when each point is constrained to a ball centered at the origin. We derive a dual minimization problem and show strong duality holds (i.e., the resulting upper bound is tight) when some locally optimal configuration of points is affinely independent. We sketch a polynomial time algorithm for finding a near-optimal set of points.Comment: Cornell ORIE Tech Repor