A Model of Optimal Network Structure for Decentralized Nearest Neighbor Search

One of the approaches for the nearest neighbor search problem is to build a network which nodes correspond to the given set of indexed objects. In this case the search of the closest object can be thought as a search of a node in a network. A procedure in a network is called decentralized if it uses only local information about visited nodes and its neighbors. Networks, which structure allows efficient performing the nearest neighbour search by a decentralised search procedure started from any node, are of particular interest especially for pure distributed systems. Several algorithms that construct such networks have been proposed in literature. However, the following questions arise: "Are there network models in which decentralised search can be performed faster?"; "What are the optimal networks for the decentralised search?"; "What are their properties?". In this paper we partially give answers to these questions. We propose a mathematical programming model for the problem of determining an optimal network structure for decentralized nearest neighbor search. We have found an exact solution for a regular lattice of size 4x4 and heuristic solutions for sizes from 5x5 to 7x7. As a distance function we use L1 , L2 and L_inf metrics. We hope that our results and the proposed model will initiate study of optimal network structures for decentralised nearest neighbour search

On duality relations for session types

Session types are a type formalism used to describe communication protocols over private session channels. Each participant in a binary session owns one endpoint of a session channel. A key notion is that of duality: the endpoints of a session channel should have dual session types in order to guarantee communication safety. Duality relations have been independently defined in different ways and different works, without considering their effect on the type system. In this paper we systematically study the existing duality relations and some new ones, and compare them in order to understand their expressiveness. The outcome is that those relations are split into two groups, one related to the na¨ıve inductive duality, and the other related to a notion of mutual compliance, which we borrow from the literature on contracts for web-services