Locally Optimal Load Balancing

This work studies distributed algorithms for locally optimal load-balancing: We are given a graph of maximum degree $\Delta$, and each node has up to $L$ units of load. The task is to distribute the load more evenly so that the loads of adjacent nodes differ by at most $1$. If the graph is a path ($\Delta = 2$), it is easy to solve the fractional version of the problem in $O(L)$ communication rounds, independently of the number of nodes. We show that this is tight, and we show that it is possible to solve also the discrete version of the problem in $O(L)$ rounds in paths. For the general case ($\Delta > 2$), we show that fractional load balancing can be solved in $\operatorname{poly}(L,\Delta)$ rounds and discrete load balancing in $f(L,\Delta)$ rounds for some function $f$, independently of the number of nodes.Comment: 19 pages, 11 figure

Tight local approximation results for max-min linear programs

In a bipartite max-min LP, we are given a bipartite graph \myG = (V \cup I \cup K, E), where each agent $v \in V$ is adjacent to exactly one constraint $i \in I$ and exactly one objective $k \in K$. Each agent $v$ controls a variable $x_v$. For each $i \in I$ we have a nonnegative linear constraint on the variables of adjacent agents. For each $k \in K$ we have a nonnegative linear objective function of the variables of adjacent agents. The task is to maximise the minimum of the objective functions. We study local algorithms where each agent $v$ must choose $x_v$ based on input within its constant-radius neighbourhood in \myG. We show that for every $\epsilon>0$ there exists a local algorithm achieving the approximation ratio ${\Delta_I (1 - 1/\Delta_K)} + \epsilon$. We also show that this result is the best possible -- no local algorithm can achieve the approximation ratio ${\Delta_I (1 - 1/\Delta_K)}$. Here $\Delta_I$ is the maximum degree of a vertex $i \in I$, and $\Delta_K$ is the maximum degree of a vertex $k \in K$. As a methodological contribution, we introduce the technique of graph unfolding for the design of local approximation algorithms.Comment: 16 page

Local algorithms : Self-stabilization on speed

Non peer reviewe

A local 2-approximation algorithm for the vertex cover problem

We present a distributed 2-approximation algorithm for the minimum vertex cover problem. The algorithm is deterministic, and it runs in (Δ + 1)2 synchronous communication rounds, where Δ is the maximum degree of the graph. For Δ = 3, we give a 2-approximation algorithm also for the weighted version of the problem.Peer reviewe

Automating and simplifying agreement and secrecy verification using PVS

In this thesis we present a system for assisting with theorem proving of security protocols. The desirability of theorem proving is examined and a method of automating the encoding, and some sections of the proof, are demonstrated. We also discuss various aspects of two different classes of security properties: secrecy and agreement. We demonstrate how our system can be used via two case study protocols, NetBill and SET. The proof can be decomposed into various sub-lemmas, most of which can be proven automatically, and then used to simplify the proofs of the final theorems of interest

P.: Load balancing by distributed optimisation in ad hoc networks

Abstract. We approach the problem of load balancing for wireless multi-hop networks by distributed optimisation. We implement an approximation algorithm for minimising the maximum network congestion as a modification to the DSR routing protocol. The algorithm is based on shortest-path computations that are integrated into the DSR route discovery and maintenance process. The resulting Balanced Multipath Source Routing (BMSR) protocol does not need to disseminate global information throughout the network. Our simulations with the ns2 simulator show a gain of 14 % to 69 % in the throughput, depending on the setup, compared to DSR for a high network load.

Transferring knowledge of activity recognition across sensor networks

A problem in performing activity recognition on a large scale (i.e. in many homes) is that a labelled data set needs to be recorded for each house activity recognition is performed in. This is because most models for activity recognition require labelled data to learn their parameters. In this paper we introduce a transfer learning method for activity recognition which allows the use of existing labelled data sets of various homes to learn the parameters of a model applied in a new home. We evaluate our method using three large real world data sets and show our approach achieves good classification performance in a home for which little or no labelled data is available