This paper presents a self-stabilizing algorithm to color the edges of a bipartite network such that any two adjacent edges receive distinct colors. The algorithm has the self-stabilizing property; it works without initializing the system. It also works in a de-centralized way without a leader computing a proper coloring for the whole system. Moreover, it finds an optimal edge coloring and its time complexity is O(n 2 k + m) moves, where k is the number of edges that are not properly colored in the initial configuration.

Starting from volume 21, I have taken the job of editor-inchief for Distributed Computing. This issue includes the first papers accepted with me at the helm. Distributed Computing is proud of the quality of papers it publishes, achieved through thorough reviewing and editorial procedures. Vassos Hadzilacos, the former editor-inchief, has been instrumental in enhancing the quality of this process and for making the journal what it is. I would like to thank Vassos for his contribution to the community, through his role in the journal, and for helping me make a smooth transition. The editorial board has changed as well. Two long-time editors, Mohamed Gouda and John McLean, have left the board. We owe them a lot for their service to the journal.

We prove that with high probability a skip graph contains a 4-regular expander as a subgraph and estimate the quality of the expansion via simulations. As a consequence, skip graphs contain a large connected component even after an adversarial deletion of nodes. We show how the expansion property can be used to sample a node in the skip graph in a highly efficient manner. We also show that the expansion property can be used to load balance the skip graph quickly. Finally, it is shown that the skip graph could serve as an unstructured P2P system, making it a good candidate for a hybrid P2P system.

Fast algorithms are presented for performing computations in a probabilistic population model. This is a variant of the standard population protocol model, in which finite-state agents interact in pairs under the control of an adversary scheduler, where all pairs are equally likely to be chosen for each interaction. It is shown that when a unique leader agent is provided in the initial population, the population can simulate a virtual register machine with high probability in which standard arithmetic operations like comparison, addition, subtraction, and multiplication and division by constants can be simulated in O(n log5 n) interactions using a simple register representation or in O(n log2 n) interactions using a more sophisticated representation that requires an extra O(n log O(1) n)-interaction initialization step. The central method is the extensive use of epidemics to propagate information from and to the leader, combined with an epidemic-based phase clock used to detect when these epidemics are likely to be complete. Applications include a reduction of the cost of computing a semilinear predicate to O(n log5 n) interactions from the previously best-known bound of O(n 2 log n) interactions and simulation of a LOGSPACE Turing machine using O(n log2 n) interactions per step after an initial O(n log O(1) n)-interaction startup phase. These bounds on interactions translate into polylogarithmic time per step in a natural parallel model in which each agent participates in an expected Θ(1) interactions per time unit. Open problems are discussed, together with simulation results that suggest the possibility of removing the initial-leader assumption.

We compare the impact of timing conditions on implementing sequentially consistent and linearizable counters using (uniform) counting networks in distributed systems. For counting problems in application domains which do not require linearizability but will run correctly if only sequential consistency is provided, the results of our investigation, and their potential payoffs, are threefold: First, we show that sequential consistency and linearizability cannot be distinguished by the timing conditions previously considered in the context of counting networks; thus, in contexts where these constraints apply, it is possible to rely on the stronger semantics of linearizability, which simplifies proofs and enhances compositionality. Second, we identify local timing conditions that support sequential consistency but not linearizability; thus, we suggest weaker, easily implementable timing conditions that are likely to be sufficient in many applications. Third, we show that any kind of synchronization that is too weak to support even sequential consistency may violate it significantly for some counting networks; hence, we identify timing conditions that are to be totally ruled out for specific applications that rely critically on either sequential consistency or linearizability.

Agreement among the processes in a distributed system is a fundamental requirement for a wide range of applications. Many forms of coordination require the processes to exchange information to negotiate with one another and eventually reach a common understanding or agreement, before taking application-specific actions. A classical example is that of the commit decision in database systems, wherein the processes collectively decide whether to commit or abort a transaction that they participate in. In this chapter, we study the feasibility of designing algorithms to reach agreement under various system models and failure models, and, where possible, examine some representative algorithms to reach agreement.

The idea of self-stabilization in distributed computing was first proposed by Dijkstra in 1974. The concept of self-stabilization is that, regardless of its initial state, the system is guaranteed to converge to a legitimate state in a bounded amount of time by itself without any outside intervention. A non-self-stabilizing system may never reach a legitimate state or it may reach a legitimate state only temporarily. The main complication in designing a self-stabilizing distributed system is that nodes do not have a global memory that they can access instantaneoulsy. Each node must make decisions based on the local knowledge available to it and actions of all nodes must achieve a global ojective.

Distributed shared memory (DSM) is an abstraction provided to the programmer of a distributed system. It gives the impression of a single monolithic memory, as in traditional von Neumann architecture. Programmers access the data across the network using only read and write primitives, as they would in a uniprocessor system. Programmers do not have to deal with send and receive communication primitives and the ensuing complexity of dealing explicitly with synchronization and consistency in the messagepassing model. The DSM abstraction is illustrated in Figure 12.1. A part of each computer's memory is earmarked for shared space, and the remainder is private memory. To provide programmers with the illusion of a single shared address space, a memory mapping management layer is required to manage the shared virtual memory space.

Deterministic collect algorithms are presented that are adaptive to total contention and are efficient with respect to both the number of registers used and the step complexity. One of them has optimal O(k) step and O(n) space complexities, but assumes that processes’ identifiers are in O(n), where n is the total number of processes in the system and k is the total contention. The step complexity of an unrestricted name space variant of this algorithm remains O(k), but its space complexity increases to O(n 2).

Transactional Memory is a concurrent programming API in which concurrent threads synchronize via transactions (instead of locks). Although this model has mostly been studied in the context of multiprocessors, it has attractive features for distributed systems as well. In this paper, we consider the problem of implementing transactional memory in a network of nodes where communication costs form a metric. The heart of our design is a new cache-coherence protocol, called the Ballistic protocol, for tracking and moving up-to-date copies of cached objects. For constant-doubling metrics, a broad class encompassing both Euclidean spaces and growth-restricted networks, this protocol has stretch logarithmic in the diameter of the network.