A Deterministic Algorithm for the Vertex Connectivity Survivable Network Design Problem

In the vertex connectivity survivable network design problem we are given an undirected graph G = (V,E) and connectivity requirement r(u,v) for each pair of vertices u,v. We are also given a cost function on the set of edges. Our goal is to find the minimum cost subset of edges such that for every pair (u,v) of vertices we have r(u,v) vertex disjoint paths in the graph induced by the chosen edges. Recently, Chuzhoy and Khanna presented a randomized algorithm that achieves a factor of O(k^3 log n) for this problem where k is the maximum connectivity requirement. In this paper we derandomize their algorithm to get a deterministic O(k^3 log n) factor algorithm. Another problem of interest is the single source version of the problem, where there is a special vertex s and all non-zero connectivity requirements must involve s. We also give a deterministic O(k^2 log n) algorithm for this problem

Logic Programming and Logarithmic Space

We present an algebraic view on logic programming, related to proof theory and more specifically linear logic and geometry of interaction. Within this construction, a characterization of logspace (deterministic and non-deterministic) computation is given via a synctactic restriction, using an encoding of words that derives from proof theory. We show that the acceptance of a word by an observation (the counterpart of a program in the encoding) can be decided within logarithmic space, by reducing this problem to the acyclicity of a graph. We show moreover that observations are as expressive as two-ways multi-heads finite automata, a kind of pointer machines that is a standard model of logarithmic space computation

Survey of Distributed Decision

We survey the recent distributed computing literature on checking whether a given distributed system configuration satisfies a given boolean predicate, i.e., whether the configuration is legal or illegal w.r.t. that predicate. We consider classical distributed computing environments, including mostly synchronous fault-free network computing (LOCAL and CONGEST models), but also asynchronous crash-prone shared-memory computing (WAIT-FREE model), and mobile computing (FSYNC model)