Leader election in synchronous networks

Worst, best and average number of messages and running time of leader election algorithms of different distributed systems are analyzed. Among others the known characterizations of the expected number of messages for LCR algorithm and of the worst number of messages of Hirschberg-Sinclair algorithm are improve

Self-stabilizing network orientation algorithms in arbitrary rooted networks

Network orientation is the problem of assigning different labels to the edges at each processor, in a globally consistent manner. A self-stabilizing protocol guarantees that the system will arrive at a legitimate state in finite time, irrespective of the initial state of the system. Two deterministic distributed network orientation protocols on arbitrary rooted, asynchronous networks are proposed in this work. Both protocols set up a chordal sense of direction in the network. The protocols are self-stabilizing, meaning that starting from an arbitrary state, the protocols are guaranteed to reach a state in which every processor has a valid node label and every link has a valid edge label. The first protocol assumes an underlying depth-first token circulation protocol; it orients the network as the token is passed among the nodes and stabilizes in O(n) steps after the token circulation stabilizes, where n is the number of processors in the network. The second protocol is designed on an underlying spanning tree protocol and stabilizes in O(h) time, after the spanning tree is constructed, where h is the height of the spanning tree. Although the second protocol assumes the existence of a spanning tree of the rooted network, it orients all edges--both tree and non-tree edges--of the network

Symmetries and sense of direction in labeled graphs

AbstractWe consider edge-labeled graphs which model distributed systems, focus on properties of edge-labelings, and study their impact on graph classes. In particular, we investigate the relation between symmetries, topologies and sense of direction. We study symmetries based on the notion of view and of surrounding, and characterize the corresponding graph classes. Among other results, we show that the completely surrounding symmetric labeled graphs coincides with the class of Cayley graphs with Cayley labelings. We then focus on the relationship between symmetries and sense of direction in regular graphs. We characterize the class of regular labeled graphs with minimal symmetric sense of direction, as well as the class of those with group-based sense of direction