A tight lower bound for steiner orientation

In the STEINER ORIENTATION problem, the input is a mixed graph G (it has both directed and undirected edges) and a set of k terminal pairs T. The question is whether we can orient the undirected edges in a way such that there is a directed s⇝t path for each terminal pair (s,t)∈T. Arkin and Hassin [DAM’02] showed that the STEINER ORIENTATION problem is NP-complete. They also gave a polynomial time algorithm for the special case when k=2 . From the viewpoint of exact algorithms, Cygan, Kortsarz and Nutov [ESA’12, SIDMA’13] designed an XP algorithm running in nO(k) time for all k≥1. Pilipczuk and Wahlström [SODA ’16] showed that the STEINER ORIENTATION problem is W[1]-hard parameterized by k. As a byproduct of their reduction, they were able to show that under the Exponential Time Hypothesis (ETH) of Impagliazzo, Paturi and Zane [JCSS’01] the STEINER ORIENTATION problem does not admit an f(k)⋅no(k/logk) algorithm for any computable function f. That is, the nO(k) algorithm of Cygan et al. is almost optimal. In this paper, we give a short and easy proof that the nO(k) algorithm of Cygan et al. is asymptotically optimal, even if the input graph has genus 1. Formally, we show that the STEINER ORIENTATION problem is W[1]-hard parameterized by the number k of terminal pairs, and, under ETH, cannot be solved in f(k)⋅no(k) time for any function f even if the underlying undirected graph has genus 1. We give a reduction from the GRID TILING problem which has turned out to be very useful in proving W[1]-hardness of several problems on planar graphs. As a result of our work, the main remaining open question is whether STEINER ORIENTATION admits the “square-root phenomenon” on planar graphs (graphs with genus 0): can one obtain an algorithm running in time f(k)⋅nO(k√) for PLANAR STEINER ORIENTATION, or does the lower bound of f(k)⋅no(k) also translate to planar graphs

Deafening silence? Marxism, international historical sociology and the spectre of Eurocentrism

Approaching the centenary of its establishment as a formal discipline, International Relations today challenges the ahistorical and aspatial frameworks advanced by the theories of earlier luminaries. Yet, despite a burgeoning body of literature built on the transdisciplinary efforts bridging International Relations and its long-separated nomothetic relatives, the new and emerging conceptual frameworks have not been able to effectively overcome the challenge posed by the ‘non-West’. The recent wave of international historical sociology has highlighted possible trajectories to problematise the myopic and unipolar conceptions of the international system; however, the question of Eurocentrism still lingers in the developing research programmes. This article interjects into the ongoing historical materialist debate in international historical sociology by: (1) conceptually and empirically challenging the rigid boundaries of the extant approaches; and (2) critically assessing the postulations of recent theorising on ‘the international’, capitalist states-system/geopolitics and uneven and combined development. While the significance of the present contributions in international historical sociology should not be understated, it is argued that the ‘Eurocentric cage’ still occupies a dominant ontological position which essentially silences ‘connected histories’ and conceals the role of inter-societal relations in the making of the modern states-system and capitalist geopolitics

The co-operative university: Labour, property and pedagogy

I begin this article by discussing the recent work of academics and activists to identify the advantages and issues relating to co-operative forms of higher education, and then focus on the ‘worker co-operative’ organisational form and its applicability and suitability to the governance of and practices within higher educational institutions. Finally, I align the values and principles of worker co-ops with the critical pedagogic framework of ‘Student as Producer’. Throughout I employ the work of Karl Marx to theorise the role of labour and property in a ‘co-operative university’, drawing particularly on later Marxist writers who argue that Marx’s labour theory of value should be understood as a critique of labour under capitalism, rather than one developed from the standpoint of labour