Better Guarantees for k-Means and Euclidean k-Median by Primal-Dual Algorithms

bibsource: dblp computer science bibliography, http://dblp.org biburl: http://dblp.org/rec/bib/conf/focs/AhmadianNSW17 timestamp: Thu, 16 Nov 2017 15:01:42 +0100 bdsk-url-1: https://doi.org/10.1109/FOCS.2017.15 bdsk-url-2: http://dx.doi.org/10.1109/FOCS.2017.15bibsource: dblp computer science bibliography, http://dblp.org biburl: http://dblp.org/rec/bib/conf/focs/AhmadianNSW17 timestamp: Thu, 16 Nov 2017 15:01:42 +0100 bdsk-url-1: https://doi.org/10.1109/FOCS.2017.15 bdsk-url-2: http://dx.doi.org/10.1109/FOCS.2017.1

Better Guarantees for kk-Means and Euclidean kk-Median by Primal-Dual Algorithms

Clustering is a classic topic in optimization with $k$-means being one of the most fundamental such problems. In the absence of any restrictions on the input, the best-known algorithm for $k$-means in Euclidean space with a provable guarantee is a simple local search heuristic yielding an approximation guarantee of $9+\epsilon$, a ratio that is known to be tight with respect to such methods. We overcome this barrier by presenting a new primal-dual approach that allows us to (1) exploit the geometric structure of $k$-means and (2) satisfy the hard constraint that at most $k$ clusters are selected without deteriorating the approximation guarantee. Our main result is a 6.357-approximation algorithm with respect to the standard linear programming (LP) relaxation. Our techniques are quite general, and we also show improved guarantees for $k$-median in Euclidean metrics and for a generalization of $k$-means in which the underlying metric is not required to be Euclidean

Non-conventional sources of agricultural water management : Insights from young professionals in the irrigation and drainage sector

Distribution and availability of global resources is highly variable over time and heterogeneous in space. With the natural or conventional supply of these resources no longer meeting a growing demand, the need to promote resource efficiency is now being paralleled with innovative approaches to conserve resources within their use cycle. These ‘innovative approaches’ herewith referred to as non-conventional was the subject of a 10-weeks extensive discussion among Young Professionals (YPs) in the field of irrigation and drainage. The discussion aligns to a higher objective of breeding a generation of YPs with an open mindset and multi-disciplinary approach to the challenges in irrigation and drainage. Cutting across development corridors in the water sector, this review paper presents insights on non-conventional sources of agricultural water management (AWM) as viewed from the lenses of YPs. The discussions underscore the need for broad-based approaches to resource management, building on the premise that all forms of resources are linked to form a system that provides the most effective service when managed in an integrated fashion. Non-conventional requires divergent approaches and flexibility; underlining the invaluable capabilities YPs present in AWM. Besides highlighting these roles, insights provided by YPs suggests that feeding a growing population necessitates looking beyond system efficiency to multivariate approaches of resource optimisation and utilisation in the field of irrigation and drainage