Robust algorithms with polynomial loss for near-unanimity CSPs

An instance of the Constraint Satisfaction Problem (CSP) is given by a family of constraints on overlapping sets of variables, and the goal is to assign values from a xed domain to the variables so that all constraints are satised. In the optimization version, the goal is to maximize the number of satised constraints. An approximation algorithm for CSP is called robust if it outputs an assignment satisfying an (1????g("))-fraction of constraints on any (1????")-satisable instance, where the loss function g is such that g(") ! 0 as " ! 0. We study how the robust approximability of CSPs depends on the set of constraint relations allowed in instances, the so-called constraint language. All constraint languages admitting a robust polynomial-time algorithm (with some g) have been characterised by Barto and Kozik, with the general bound on the loss g being doubly exponential, specically g(") = O((log log(1="))= log(1=")). It is natural to ask when a better loss can be achieved: in particular, polynomial loss g(") = O("1=k) for some constant k. In this paper, we consider CSPs with a constraint language having a nearunanimity polymorphism. This general condition almost matches a known necessary condition for having a robust algorithm with polynomial loss. We give two randomized robust algorithms with polynomial loss for such CSPs: one works for any near-unanimity polymorphism and the parameter k in the loss depends on the size of the domain and the arity of the relations in ????, while the other works for a special ternary near-unanimity operation called dual discriminator with k = 2 for any domain size. In the latter case, the CSP is a common generalisation of Unique Games with a xed domain and 2-Sat. In the former case, we use the algebraic approach to the CSP. Both cases use the standard semidenite programming relaxation for CSP

Min-max graph partitioning and small set expansion

We study graph partitioning problems from a min-max perspective, in which an input graph on n vertices should be partitioned into k parts, and the objective is to minimize the maximum number of edges leaving a single part. The two main versions we consider are where the k parts need to be of equal-size, and where they must separate a set of k given terminals. We consider a common generalization of these two problems, and design for it an $O(\sqrt{\log n\log k})$-approximation algorithm. This improves over an $O(\log^2 n)$ approximation for the second version, and roughly $O(k\log n)$ approximation for the first version that follows from other previous work. We also give an improved O(1)-approximation algorithm for graphs that exclude any fixed minor. Our algorithm uses a new procedure for solving the Small-Set Expansion problem. In this problem, we are given a graph G and the goal is to find a non-empty set $S\subseteq V$ of size $|S| \leq \rho n$ with minimum edge-expansion. We give an $O(\sqrt{\log{n}\log{(1/\rho)}})$ bicriteria approximation algorithm for the general case of Small-Set Expansion, and O(1) approximation algorithm for graphs that exclude any fixed minor

Politicising government engagement with corporate social responsibility: “CSR” as an empty signifier

Governments are widely viewed by academics and practitioners (and society more generally) as the key societal actors who are capable of compelling businesses to practice corporate social responsibility (CSR). Arguably, such government involvement could be seen as a technocratic device for encouraging ethical business behaviour. In this paper, we offer a more politicised interpretation of government engagement with CSR where “CSR” is not a desired form of business conduct but an element of discourse that governments can deploy in structuring their relationships with other social actors. We build our argument through a historical analysis of government CSR discourse in the Russian Federation. Laclau and Mouffe's (Hegemony and socialist strategy: Towards a radical democratic politics,Verso Books, London, 1985) social theory of hegemony underpins our research. We find that “CSR” in the Russian government’s discourse served to legitimise its power over large businesses. Using this case, we contribute to wider academic debates by providing fresh empirical evidence that allows the development of critical evaluation tools in relation to governments’ engagement with “CSR”. We find that governments are capable of hijacking CSR for their own self-interested gain. We close the paper by reflecting on the merit of exploring the case of the Russian Federation. As a “non-core”, non-western exemplar, it provides a useful “mirror” with which to reflect on the more widely used test-bed of Western industrial democracies when scrutinising CSR. Based on our findings, we invite other scholars to adopt a more critical, politicised stance when researching the role of governments in relation to CSR in other parts of the world

Min-max graph partitioning and small set expansion

We study graph partitioning problems from a min-max perspective, in which an input graph on $n$ vertices should be partitioned into $k$ parts, and the objective is to minimize the maximum number of edges leaving a single part. The two main versions we consider are where the $k$ parts need to be of equal size, and where they must separate a set of $k$ given terminals. We consider a common generalization of these two problems, and design for it an $O(\sqrt{\log n\log k})$ approximation algorithm. This improves over an $O(\log^2 n)$ approximation for the second version due to Svitkina and Tardos [Min-max multiway cut, in APPROX-RANDOM, 2004, Springer, Berlin, 2004], and roughly $O(k\log n)$ approximation for the first version that follows from other previous work. We also give an $O(1)$ approximation algorithm for graphs that exclude any fixed minor. Our algorithm uses a new procedure for solving the small-set expansion problem. In this problem, we are given a graph $G$ and the goal is to find a nonempty set $S\subseteq V$ of size $|S| \leq \rho n$ with minimum edge expansion. We give an $O(\sqrt{\log{n}\log{(1/\rho)}})$ bicriteria approximation algorithm for small-set expansion in general graphs, and an improved factor of $O(1)$ for graphs that exclude any fixed minor

Min-max graph partitioning and small set expansion

We study graph partitioning problems from a min-max perspective, in which an input graph on $n$ vertices should be partitioned into $k$ parts, and the objective is to minimize the maximum number of edges leaving a single part. The two main versions we consider are where the $k$ parts need to be of equal size, and where they must separate a set of $k$ given terminals. We consider a common generalization of these two problems, and design for it an $O(\sqrt{\log n\log k})$ approximation algorithm. This improves over an $O(\log^2 n)$ approximation for the second version due to Svitkina and Tardos [Min-max multiway cut, in APPROX-RANDOM, 2004, Springer, Berlin, 2004], and roughly $O(k\log n)$ approximation for the first version that follows from other previous work. We also give an $O(1)$ approximation algorithm for graphs that exclude any fixed minor. Our algorithm uses a new procedure for solving the small-set expansion problem. In this problem, we are given a graph $G$ and the goal is to find a nonempty set $S\subseteq V$ of size $|S| \leq \rho n$ with minimum edge expansion. We give an $O(\sqrt{\log{n}\log{(1/\rho)}})$ bicriteria approximation algorithm for small-set expansion in general graphs, and an improved factor of $O(1)$ for graphs that exclude any fixed minor

The missing link in human security research: dialogue and insecurity in Kosovo

The concept of human security continues to defy definitional clarity at the same time as it is being embraced by policymakers. This article proposes a practice-grounded approach that focuses on investigative method as a way of linking conceptual understanding of human security to the research process. Probing the 'actorness' of individuals in volatile contexts, a study of insecurity in Kosovo shows how dialogue can be applied as a research tool to access and assess human security in the field. Dialogue permits recognition of the power of the researched in the construction of knowledge of security, and accordingly reflects the conceptual shift represented by human security from states to communities and individuals. In the Kosovo study, dialogic research captured individual agency in the face of pervasive insecurity and revealed contradictory effects of such agency. This led to the formulation of the idea of the multidirectional security marker as a means of understanding experiences of insecurity in relation to strategies to combat it. Three such markers - self-reliance, informality and community solidarity - emerged and are analysed in the case of Kosovo. Simultaneously denoting restrictions on people's security and possibilities for overcoming those very same limitations, the markers express the agential dimension of human security and show how agency and security interact