For overlay networks, the ability to recover from a variety of problems like membership changes or faults is a key element to preserve their functionality. In recent years, various self-stabilizing overlay networks have been proposed that have the advantage of being able to recover from any illegal state. However, the vast majority of these networks cannot give any guarantees on its functionality while the recovery process is going on. We are especially interested in searchability, i.e., the functionality that search messages for a specific identifier are answered successfully if a node with that identifier exists in the network. We investigate overlay networks that are not only self-stabilizing but that also ensure that monotonic searchability is maintained while the recovery process is going on, as long as there are no corrupted messages in the system. More precisely, once a search message from node u to another node v is successfully delivered, all future search messages from u to v succeed as well. Monotonic searchability was recently introduced in OPODIS 2015, in which the authors provide a solution for a simple line topology. We present the first universal approach to maintain monotonic searchability that is applicable to a wide range of topologies. As the base for our approach, we introduce a set of primitives for manipulating overlay networks that allows us to maintain searchability and show how existing protocols can be transformed to use theses primitives. We complement this result with a generic search protocol that together with the use of our primitives guarantees monotonic searchability. As an additional feature, searching existing nodes with the generic search protocol is as fast as searching a node with any other fixed routing protocol once the topology has stabilized.

Network creation games model the creation and usage costs of networks formed by a set of selfish peers. Each peer has the ability to change the network in a limited way, e.g., by creating or deleting incident links. In doing so, a peer can reduce its individual communication cost. Typically, these costs are modeled by the maximum or average distance in the network. We introduce a generalized version of the basic network creation game (BNCG). In the BNCG (by Alon et al., SPAA 2010), each peer may replace one of its incident links by a link to an arbitrary peer. This is done in a selfish way in order to minimize either the maximum or average distance to all other peers. That is, each peer works towards a network structure that allows himself to communicate efficiently with all other peers. However, participants of large networks are seldom interested in all peers. Rather, they want to communicate efficiently only with a small subset of peers. Our model incorporates these (communication) interests explicitly. In the MAX-version, each node tries to minimize its maximum distance to nodes it is interested in. Likewise, the goal of each node in the AVG-version is to minimize the corresponding average distance.Given peers with interests and a communication network forming a tree, we prove several results on the structure and quality of equilibria in our model. For the MAX-version, we give an upper worst case bound of O ( √ n) for the private costs in an equilibrium of n peers. Moreover, we give an equilibrium for a circular interest graph where a node has private cost Ω ( √ n), showing that our bound is tight. This example can be extended such that we get a tight bound of Θ ( √ n) for the price of anarchy. For the case of general communication networks we show the price of anarchy to be Θ (n). Additionally, we prove an interesting connection between a maximum independent set in the interest graph and the private costs of the peers. For the AVG-version, we give a linear lower bound on the worst case private costs in an equilibrium.In a network creation game (NCG), several selfish players create a network by egoistic modifications of its edges. One of the most famous NCG models is due to Fabrikant et al. [6]. Their model intends to capture the dynamics in large communication and computer networks built by the individual participants (peers, players) in a selfish way: participants try to ensure a network structure supporting their own communication needs whilst limiting their individual investment into the network. Since the players do not (necessarily) cooperate, the resulting network structure may be suboptimal from a global point of view. The analysis of the resulting structure and its comparison to a (socially) optimal structure is a central aspect in the analysis of network creation games.In the original model by Fabrikant et al., players may buy (or create) a single edge for a certain (fixed) cost of α > 0. Their goal when buying edges is to improve the network structure with respect to their individual communication ...

No abstract

We present a factor 14D 2 approximation algorithm for the minimum linear arrangement problem on series-parallel graphs, where D is the maximum degree in the graph. Given a suitable decomposition of the graph, our algorithm runs in time O(|E|) and is very easy to implement. Its divide-andconquer approach allows for an effective parallelization. Note that a suitable decomposition can also be computed in time O(|E| log |E|) (or even O(log |E| log * |E|) on an EREW PRAM using O(|E|) processors). For the proof of the approximation ratio, we use a sophisticated charging method that uses techniques similar to amortized analysis in advanced data structures.On general graphs, the minimum linear arrangement problem is known to be NP-hard. To the best of our knowledge, the minimum linear arrangement problem on series-parallel graphs has not been studied before.