How to detect a counterfeit coin: Adaptive versus non-adaptive solutions

In an old weighing puzzle, there are n3 coins that are identical in appearance. All the coins except one have the same weight, and that counterfeit one is a little bit lighter or heavier than the others, though it is not known in which direction. What is the smallest number of weighings needed to identify the counterfeit coin and to determine its type, using balance scales without measuring weights? This question was fully answered in 1946 by Dyson [The Mathematical Gazette 30 (1946) 231–234]. For values of n that are divisible by three, Dyson's scheme is non-adaptive and hence its later weighings do not depend on the outcomes of its earlier weighings. For values of n that are not divisible by three, however, Dyson's scheme is adaptive. In this note, we show that for all values n3 there exists an optimal weighing scheme that is non-adaptive

On k-Column Sparse Packing Programs

We consider the class of packing integer programs (PIPs) that are column sparse, i.e. there is a specified upper bound k on the number of constraints that each variable appears in. We give an (ek+o(k))-approximation algorithm for k-column sparse PIPs, improving on recent results of $k^2\cdot 2^k$ and $O(k^2)$. We also show that the integrality gap of our linear programming relaxation is at least 2k-1; it is known that k-column sparse PIPs are $\Omega(k/ \log k)$-hard to approximate. We also extend our result (at the loss of a small constant factor) to the more general case of maximizing a submodular objective over k-column sparse packing constraints.Comment: 19 pages, v3: additional detail

Some Varieties of Equational Logic (Extended Abstract)

... been a major theme of Joseph Goguen’s research, perhaps even the major theme. One strand of this work concerns algebraic datatypes. Recently there has been some interest in what one may call algebraic computation types. As we will show, these are also given by equational theories, if one only understands the notion of equational logic in somewhat broader senses than usual. One moral of our work is that, suitably considered, equational logic is not tied to the usual first-order syntax of terms and equations. Standard equational logic has proved a useful tool in several branches of computer science, see, for example, the RTA conference series [9] and textbooks, such as [1]. Perhaps the possibilities for richer varieties of equational logic discussed here will lead to further applications. We begin with an explanation of computation types. Starting around 1989, Eugenio Moggi introduced the idea of monadic notions of computation [11, 12

On generation of a class of flowgraphs

We present some structure theorems for the class of binary flowgraphs. These graphs show up in the study of the structural complexity of flowcharts. A binary flowgraph is a digraph with distinct vertices s and t such that (1) t is a sink, (2) all vertices other than t have outdegree 2 and (3) for every vertex v there is a path from s to v, and a path from v to t. An irreducible flowgraph (IBF) is a binary flowgraph with no proper subgraph that is a binary flowgraph. We define a simple operation called generation that produces an IBF on k vertices from one on k - 1 vertices. Our main result is that all IBF's can be obtained from an IBF on two vertices by a sequence of generation operations. In some cases the last generation step is uniquely defined and we give some additional results on this matter

On the nearest neighbor rule for the traveling salesman problem

Rosenkrantz et al. (SIAM J. Comput. 6 (1977) 563) and Johnson and Papadimitriou (in: E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan, D.B. Shmoys (Eds.), The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization, Wiley, Chichester, 1985, pp. 145–180, (Chapter 5)) constructed families of TSP instances with n cities for which the nearest neighbor rule yields a tour-length that is a factor Ω(log n) above the length of the optimal tour.\ud \ud We describe two new families of TSP instances, for which the nearest neighbor rule shows the same bad behavior. The instances in the first family are graphical, and the instances in the second family are Euclidean. Our construction and our arguments are extremely simple and suitable for classroom use

On generation of a class of flowgraphs

We present some structure theorems for the class of binary flowgraphs. These graphs show up in the study of the structural complexity of flowcharts. A binary flowgraph is a digraph with distinct vertices s and t such that (1) t is a sink, (2) all vertices other than t have outdegree 2 and (3) for every vertex v there is a path from s to v, and a path from v to t. An irreducible flowgraph (IBF) is a binary flowgraph with no proper subgraph that is a binary flowgraph. We define a simple operation called generation that produces an IBF on k vertices from one on k - 1 vertices. Our main result is that all IBF's can be obtained from an IBF on two vertices by a sequence of generation operations. In some cases the last generation step is uniquely defined and we give some additional results on this matter

Alternatieve grondontsmetting : Interview met Wenneker, Visser en Korthals

Herinplantziekte of bodemmoeheid is op zandgronden één van de grootste problemen bij de herinplant van een appelperceel. Natte grondonstsmetting biest een oplossing, maar de vraag is of dit de beste methode is. PPO zoekt naar alternatieven