Sven Köhler

A new technique for proving self-stabilizing under the distributed scheduler

Proving stabilization of a complex algorithm under the distributed scheduler is a non-trivial task. This paper introduces a new method which allows to extend proofs for the central scheduler to the distributed scheduler. The practicability of the method is shown by applying it to two existing algorithms, for which stabilization under the distributed scheduler was an open problem.

Fault-containing self-stabilization in asynchronous systems with constant fault-gap

This paper presents a new transformation which adds fault-containment properties to silent self-stabilizing algorithms. The transformation features a constant slow-down factor and the fault-gap—that is the minimal time between two containable faults—is also constant. The transformation scales well to arbitrarily large systems and avoids global synchronization. The presented transformation is the first with a constant fault-gap and requires no knowledge of the system size.

Fault-Containing Self-Stabilization in Asynchronous Systems with Constant Fault-Gap

This paper presents a new transformation which adds fault-containment properties to any silent self-stabilizing protocol. The transformation features a constant slow-down factor and the fault-gap – that is the minimal time between two containable faults – is constant. The transformation scales well to arbitrarily large systems and avoids global synchronization.

A Distributed Algorithm for Minimum Distance-k Domination in Trees

While ecient algorithms for finding minimal distancek dominating sets exist, finding minimum such sets is NP-hard even for bipartite graphs. This paper presents a distributed algorithm to determine a minimum (connected) distance-k dominating set and a maximum distance-2k independent set of a tree T. It terminates in O(height(T)) rounds and uses O(logk) space. To the best of our knowledge this is the first distributed algorithm that computes a minimum (as opposed to a minimal) distancek dominating set for trees. The algorithm can also be applied to general graphs, albeit the distance-k dominating sets are not necessarily minimal.

Distributed Backup Placement in Networks

We consider the backup placement problem, defined as follows. Some nodes (processors) in a given network have objects (e.g., files, tasks) whose backups should be stored in additional nodes for increased fault resilience. To minimize the disturbance in case of a failure, it is required that a backup copy should be located at a neighbor of the primary node. The goal is to find an assignment of backup copies to nodes which minimizes the maximum load (number or total size of copies) over all nodes in the network. It is known that a natural selfish local improvement policy has approximation ratio Ω(log n / log log n); we show that it may take this policy Ω(√n) time to reach equilibrium in the distributed setting. Our main result in this paper is a distributed algorithm which finds a placement in polylogarithmic time and achieves approximation ratio O(log n/log log n). We obtain this result using a distributed approximation algorithm for f-matching in bipartite graphs that may be of independent interest.

Self-stabilizing local k -placement of replicas with minimal variance

Large scale distributed systems require replication of resources to amplify availability and to provide fault tolerance. The placement of replicated resources significantly impacts performance. This paper considers local k-placements: Each node of a network has to place k replicas of a resource among its direct neighbors. The load of a node in a given local k-placement is the number of replicas it stores. The local k-placement problem is to achieve a preferably homogeneous distribution of the loads. We present a novel self-stabilizing, distributed, asynchronous, scalable algorithm for the k-placement problem such that the standard deviation of the distribution of the loads assumes a local minimum.

Space-efficient fault-containment in dynamic networks

Bounding the impact of transient small-scale faults by self-stabilizing protocols has been pursued with independent objectives: Optimizing the systems reaction upon topological changes (e.g. super-stabilization), and reducing system recovery time from memory corruptions (e.g. fault-containment). Even though transformations adding either super-stabilization or fault-containment to existing protocols exist, none of them preserves the other. This paper makes a first attempt to combine both objectives. We provide a transformation adding faultcontainment to silent self-stabilizing protocols while simultaneously preserving the property of self-stabilization and the protocols behavior in face of topological changes. In particular, the protocols response to a topology change remains unchanged even if a memory corruption occurs in parallel to the topology change. The presented transformation increases the memory footprint only by a factor of 4 and adds O(1) bits per edge. All previously known transformations for faultcontaining self-stabilization increase the memory footprint by a factor of 2m/n.

Distributed approximation of k -service assignment

We consider the k-Service Assignment problem (

Distributed Approximation of k-Service Assignment

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