Locally Self-Adjusting Skip Graphs

We present a distributed self-adjusting algorithm for skip graphs that minimizes the average routing costs between arbitrary communication pairs by performing topological adaptation to the communication pattern. Our algorithm is fully decentralized, conforms to the $\mathcal{CONGEST}$ model (i.e. uses $O(\log n)$ bit messages), and requires $O(\log n)$ bits of memory for each node, where $n$ is the total number of nodes. Upon each communication request, our algorithm first establishes communication by using the standard skip graph routing, and then locally and partially reconstructs the skip graph topology to perform topological adaptation. We propose a computational model for such algorithms, as well as a yardstick (working set property) to evaluate them. Our working set property can also be used to evaluate self-adjusting algorithms for other graph classes where multiple tree-like subgraphs overlap (e.g. hypercube networks). We derive a lower bound of the amortized routing cost for any algorithm that follows our model and serves an unknown sequence of communication requests. We show that the routing cost of our algorithm is at most a constant factor more than the amortized routing cost of any algorithm conforming to our computational model. We also show that the expected transformation cost for our algorithm is at most a logarithmic factor more than the amortized routing cost of any algorithm conforming to our computational model

A P2P Sensor Data Stream Delivery System to Accommodate Heterogeneous Cycles Using Skip Graphs

3PGCIC2015 : 10th International Conference on P2P, Parallel, Grid, Cloud and Internet Computing , Nov 4-6, 2015 , Krakow, PolandIn this paper, we propose a method using skip graphs to delivery sensor data streams with heterogeneous delivery cycles. Currently skip graphs have been proposed as one of structured overlay networks that construct links among nodes based on a specific rule. The proposed method sorts nodes by their delivery cycles and constructs delivery paths based on skip graphs. We confirmed in simulation that our proposed method can delivery sensor data with heterogeneous cycles using skip graphs to distribute the load of source node

Multi-Dimensional Range Querying using a Modification of the Skip Graph

Skip graphs are an application layer-based distributed routing data structure that can be used in a sensor network to facilitate user queries of data collected by the sensor nodes. This research investigates the impact of a proposed modification to the skip graph proposed by Aspnes and Shah. Nodes contained in a standard skip graph are sorted by their key value into successively smaller groups based on random membership vectors computed locally at each node. The proposed modification inverts the node key and membership vector roles, where group membership is computed deterministically and node keys are computed randomly. Both skip graph types are modeled in Java. Range query and node mobility simulations are performed. The number of skip graph levels, total node count, and query precision are varied for query simulations; number of levels and total node count is varied for the mobility simulation. Query performance is measured by the number of skip graph messages used to execute the query while mobility performance is measured by the number of messages transmitted to maintain skip graph coherence. When the number of levels is limited and query precision is low, or when query precision is matched by the number of levels in the skip graph and total network node counts are increased, the modified skip graph transmits fewer messages to execute the query. Furthermore, fewer update messages are needed to fix lost node references due to mobile nodes