This work is motivated by an application in local access network design that can be modeled using the KP-hard Prize Collecting Steiner Tree problem. We consider several variants on this problem and on the primal-dual 2-approximation algorithm devised for it by Goemans and Williamson. We develop several modifications to the algorithm which lead to theoretical as well as practical improvements in...

Timothy Williamson holds that vagueness, properly understood, is an epistemic phenomenon: vague terms and concepts have precise boundaries of correct applicability and non-applicability, but humans are necessarily ignorant of the locations of these boundaries. Williamson argues that our ignorance of boundary locations, and our inability to imagine recognizing a transition as a transition, are p...

We study the behavior of an algorithm derived from the cavity method for the prize-collecting steiner tree (PCST) problem on graphs. The algorithm is based on the zero temperature limit of the cavity equations and as such is formally simple (a fixed point equation resolved by iteration) and distributed (parallelizable). We provide a detailed comparison with state-of-the-art algorithms on a wide...

The object of the present essay is neither to overturn transaction cost economics nor to deny the reality of opportunism. Instead, it is to question the explanatory role of the concept of opportunism in the transaction cost analysis of Oliver Williamson and his followers. Williamson has suggested that potential or actual opportunism emerges as the source of the ‘transaction costs’ involved in m...

This paper uses the concept of organisational field as a tool for comparative research exploring the role of non-profit organisations in the provision of housing to low income households in Ireland’s two jurisdictions. Further comparison is provided between these two ‘non-profit housing systems’ and that found in England. The paper draws on preliminary research undertaken by the authors in each...

In the generalized Steiner tree problem, we find a minimumcost set of edges to connect a given set of source-sink pairs. In the online version of this problem, the source-sink pairs arrive over time. Agrawal, Klein, and Ravi [1] give a 2-approximation algorithm for the offline problem; Berman and Coulston [3] give an O(logn)-competitive algorithm for the online problem. Goemans and Williamson [...

We consider the problem of partitioning the vertices of a weighted graph into two sets of sizes that differ at most by a given threshold B, so as to maximize the weight of the crossing edges. For B equal to 0 this problem is known as Max Bisection, whereas for B equal to the number n of nodes it is the Maximum Cut problem. We present polynomial time randomized approximation algorithms with non ...

In his ‘Objective Bayesian calibration and the problem of non-convex evidence’, Gregory Wheeler criticises the principle I invoke in Williamson (2010) for calibrating degrees of belief with chances. Bayesian epistemologists commonly appeal to some sort of Calibration norm that says that degrees of belief should be calibrated to known chances. Typically they invoke a principle variously known as...

Orthogonal bipolar spreading sequences are used in direct sequence code division multiple access (DS-CDMA) systems for both spectrum spreading and channel separation. The most commonly used sequences are Walsh– Hadamard sequences of lengths being an integer power of 2. A construction based on Williamson’s arrays leading to sequences of lengths N:4 (mod 8) is presented in the paper. Aperiodic co...