Towards Optimal Synchronous Counting

Consider a complete communication network of $n$ nodes, where the nodes receive a common clock pulse. We study the synchronous $c$-counting problem: given any starting state and up to $f$ faulty nodes with arbitrary behaviour, the task is to eventually have all correct nodes counting modulo $c$ in agreement. Thus, we are considering algorithms that are self-stabilizing despite Byzantine failures. In this work, we give new algorithms for the synchronous counting problem that (1) are deterministic, (2) have linear stabilisation time in $f$, (3) use a small number of states, and (4) achieve almost-optimal resilience. Prior algorithms either resort to randomisation, use a large number of states, or have poor resilience. In particular, we achieve an exponential improvement in the space complexity of deterministic algorithms, while still achieving linear stabilisation time and almost-linear resilience.Comment: 17 pages, 2 figure

Large Cuts with Local Algorithms on Triangle-Free Graphs

We study the problem of finding large cuts in $d$-regular triangle-free graphs. In prior work, Shearer (1992) gives a randomised algorithm that finds a cut of expected size $(1/2 + 0.177/\sqrt{d})m$, where $m$ is the number of edges. We give a simpler algorithm that does much better: it finds a cut of expected size $(1/2 + 0.28125/\sqrt{d})m$. As a corollary, this shows that in any $d$-regular triangle-free graph there exists a cut of at least this size. Our algorithm can be interpreted as a very efficient randomised distributed algorithm: each node needs to produce only one random bit, and the algorithm runs in one synchronous communication round. This work is also a case study of applying computational techniques in the design of distributed algorithms: our algorithm was designed by a computer program that searched for optimal algorithms for small values of $d$.Comment: 1+17 pages, 8 figure

Approximating max-min linear programs with local algorithms

A local algorithm is a distributed algorithm where each node must operate solely based on the information that was available at system startup within a constant-size neighbourhood of the node. We study the applicability of local algorithms to max-min LPs where the objective is to maximise $\min_k \sum_v c_{kv} x_v$ subject to $\sum_v a_{iv} x_v \le 1$ for each $i$ and $x_v \ge 0$ for each $v$. Here $c_{kv} \ge 0$, $a_{iv} \ge 0$, and the support sets $V_i = \{v : a_{iv} > 0 \}$, $V_k = \{v : c_{kv}>0 \}$, $I_v = \{i : a_{iv} > 0 \}$ and $K_v = \{k : c_{kv} > 0 \}$ have bounded size. In the distributed setting, each agent $v$ is responsible for choosing the value of $x_v$, and the communication network is a hypergraph $\mathcal{H}$ where the sets $V_k$ and $V_i$ constitute the hyperedges. We present inapproximability results for a wide range of structural assumptions; for example, even if $|V_i|$ and $|V_k|$ are bounded by some constants larger than 2, there is no local approximation scheme. To contrast the negative results, we present a local approximation algorithm which achieves good approximation ratios if we can bound the relative growth of the vertex neighbourhoods in $\mathcal{H}$.Comment: 16 pages, 2 figure

From teleoperation to the cognitive human-robot interface

Robots are slowly moving from factories to mines, construction sites, public places and homes. This new type of robot or robotized working machine – field and service robots (FSR) – should be capable of performing different kinds of tasks in unstructured changing environments, not only among humans but through continuous interaction with humans. The main requirements for an FSR are mobility, advanced perception capabilities, high "intelligence" and easy interaction with humans. Although mobility and perception capabilities are no longer bottlenecks, they can nevertheless still be greatly improved. The main bottlenecks are intelligence and the human - robot interface (HRI). Despite huge efforts in "artificial intelligence" research, the robots and computers are still very "stupid" and there are no major advancements on the horizon. This emphasizes the importance of the HRI. In the subtasks, where high-level cognition or intelligence is needed, the robot has to ask for help from the operator. In addition to task commands and supervision, the HRI has to provide the possibility of exchanging information about the task and environment through continuous dialogue and even methods for direct teleoperation. The thesis describes the development from teleoperation to service robot interfaces and analyses the usability aspects of both teleoperation/telepresence systems and robot interfaces based on high-level cognitive interaction. The analogue in the development of teleoperation interfaces and HRIs is also pointed out. The teleoperation and telepresence interfaces are studied on the basis of a set of experiments in which the different enhancement-level telepresence systems were tested in different tasks of a driving type. The study is concluded by comparing the usability aspects and the feeling of presence in a telepresence system. HRIs are studied with an experimental service robot WorkPartner. Different kinds of direct teleoperation, dialogue and spatial information interfaces are presented and tested. The concepts of cognitive interface and common presence are presented. Finally, the usability aspects of a human service robot interface are discussed and evaluated.reviewe