Axiomatic Characterization of the Mean Function on Trees

A mean of a sequence π = (x1, x2, . . . , xk) of elements of a finite metric space (X, d) is an element x for which is minimum. The function Mean whose domain is the set of all finite sequences on X and is defined by Mean(π) = { x | x is a mean of π } is called the mean function on X. In this paper the mean function on finite trees is characterized axiomatically

Maximum gradient embeddings and monotone clustering

Let (X,d_X) be an n-point metric space. We show that there exists a distribution D over non-contractive embeddings into trees f:X-->T such that for every x in X, the expectation with respect to D of the maximum over y in X of the ratio d_T(f(x),f(y)) / d_X(x,y) is at most C (log n)^2, where C is a universal constant. Conversely we show that the above quadratic dependence on log n cannot be improved in general. Such embeddings, which we call maximum gradient embeddings, yield a framework for the design of approximation algorithms for a wide range of clustering problems with monotone costs, including fault-tolerant versions of k-median and facility location.Comment: 25 pages, 2 figures. Final version, minor revision of the previous one. To appear in "Combinatorica

When is a bed not a bed? Exploring the interplay of the material and virtual in negotiating home-work boundaries

© 2017, © 2017 Informa UK Limited, trading as Taylor & Francis Group. Working from home is often associated with possibilities of anytime-anyplace working and with a fusion of work and home. In this empirical paper, we explore how the sociomaterial contexts of home-working define and tether what is possible for home-workers in their negotiations with others. Drawing on qualitative data sets, Wengerian concepts are used by exploring the role of boundary objects and brokering in negotiating temporal and spatial boundaries around and across work and home. The home-workers’ bodies are shown to be the key boundary objects, through which technology objects and furniture objects are sometimes fused. Yet, such fusion is shown to be only temporary, always precariously situated and also mediated by identity-regulating norms and values of home-workers. The contribution of the paper is to highlight the limits of what is technologically possible by emphasising the role of the body and material objects in the home-working context