Cooperative Data Exchange based on MDS Codes

The cooperative data exchange problem is studied for the fully connected network. In this problem, each node initially only possesses a subset of the $K$ packets making up the file. Nodes make broadcast transmissions that are received by all other nodes. The goal is for each node to recover the full file. In this paper, we present a polynomial-time deterministic algorithm to compute the optimal (i.e., minimal) number of required broadcast transmissions and to determine the precise transmissions to be made by the nodes. A particular feature of our approach is that {\it each} of the $K-d$ transmissions is a linear combination of {\it exactly} $d+1$ packets, and we show how to optimally choose the value of $d.$ We also show how the coefficients of these linear combinations can be chosen by leveraging a connection to Maximum Distance Separable (MDS) codes. Moreover, we show that our method can be used to solve cooperative data exchange problems with weighted cost as well as the so-called successive local omniscience problem.Comment: 21 pages, 1 figur

Discovering cultural justice: Difference, democracy and the discursive minimal state.

In this thesis a theory of cultural justice is developed from Hayekian premises. Importantly, and despite the virtual disappearance of the centralised economic institutions that Hayek was always keen to reject, it claims that it is possible to reconnect his thought to contemporary political theory and to both critically and normatively contribute to debates about multicultural justice. For what is most interesting about Hayek today are not the reasons why he defended liberalism but rather the conceptual tools that he deployed in doing so. It is these conceptual tools that can e shown to have a relevance to contemporary concerns with cultural diversity that is methodologically, critically and normatively both clear and compelling. Part One of this thesis discusses Hayek's place in contemporary political theory. In Chapter One it is claimed that an interpretative reading of Hayek's social theory and of the conception of the self that underlies it not only clarifies his well-known economic arguments, but also enables us to appeal to his thought with respect to culture. Chapter Two builds upon this to address Hayek's normative argument for individual cultural liberty. Part Two is concerned to examine, from this Hayekian, the response to diversity of a range of theorists. In Chapter Three, the response of the difference democrats who endorse a group-differentiated account of deliberative democratic decision-making is assessed and, in Chapter Four, that of liberal egalitarian theory that both attempts and in a significant sense rejects the reconciliation of cultural difference with the institutions of the welfare state. Finally, Part Three is concerned with the account of cultural justice emergent from these discussions. Thus Chapter Five concerns itself with the articulation of the Discursive Minimal State and, in Chapter Six, with its defence against some important objections

Agaat's Law. Reflections on Law and Literature with Reference to Marlene Van Niekerk's novel Agaat

This essay explores the relation between law and literature from the literary Marxist position that Jean-Luc Nancy develops in his work La Communauté Désoeuvrée. It does so with specific reference to Marlene van Niekerk’s novel Agaat and to the Lacanian problematic of imaginary selves caught up in the confines of their speculative or mirroring images of others. It takes leave of approaches to law and literature studies such as Martha Nussbaum’s in terms of which literature can be invoked to edify or improve the law. It argues that law and literature can both benefit from a comparative exchange, provided this exchange takes seriously the fundamental and irreducible tension and hiatus between characteristically “legal” and characteristically “literary” discourses