Maria Gradinariu

Self-Stabilizing Local Mutual Exclusion and Daemon Refinement

Refining self-stabilizing algorithms which use tighter scheduling constraints (weaker daemon) into corresponding algorithms for weaker or no scheduling constraints (stronger daemon), while preserving the stabilization property, is useful and challenging. Designing transformation techniques for these refinements has been the subject of serious investigations in recent years. This paper proposes a transformation technique to achieve the above task. The heart of the transformer is a self-stabilizing local mutual exclusion algorithm. The local mutual exclusion problem is to grant a process the privilege to enter the critical section if and only if none of the neighbors of the process has the privilege. The contribution of this paper is twolold. First, we present a bounded-memory self-stabilizing local mutual exclusion algorithm for arbitrary network, assuming any arbitrary daemon. After stabilization, this algorithm maintains a bound on the service time (the delay between two successive executions of the critical section by a particular process). This bound is n×(n-1)/2 where n is the network size. Second, we use the local mutual exclusion algorithm to design two scheduler transformers which convert the algorithms working under a weaker daemon to ones which work under the distributed, arbitrary (or unfair) daemon, both transformers preserving the self-stabilizing property. The first transformer refines algorithms written under the central daemon, while the second transformer refines algorithms designed for the k-fair (k ? (n - 1)) daemon.

A Semantic Overlay for Self- Peer-to-Peer Publish/Subscribe

Publish/Subscribe systems provide a useful platform for delivering data (events) from publishers to subscribers in an anonymous fashion in distributed networks. In this paper, we promote a novel design principle for self-. dynamic and reliable content-based publish/subscribe systems and perform a comparative analysis of its probabilistic and deterministic implementations. More specifically, we present a generic content-based publish/subscribe system, called DPS (Dynamic Publish/Subscribe). DPS combines classical content-based filtering with self-. (self-organizing, selfconfiguring, and self-healing) subscription-driven clustering of subscribers. DPS gracefully adapts to failures and changes in the system while achieving scalable events delivery. DPS includes a variety of fault-tolerant deterministic and probabilistic content-based publication/subscription schemes. These schemes are targeted toward scalability, and aim at reducing and distributing the number of messages exchanged. Reliability and scalability of our system are shown through analytical and experimental evaluation.

Memory space requirements for self-stabilizing leader election protocols

We study the memory requirements of self-stabilizing leader election (SSLE) protocols. We are mainly interested in two types of systems: anonymous systems and id-based systems. We consider two classes of protocols: deterministic ones and randomized ones. We prove that a non-constant lower bound on the memory space is required by a SSLE protocol on unidirectional, anonymous rings (even if the protocol is randomized). We show that, if there is a deterministic protocol solving a problem on id-based systems where the processor memory space is constant and the id-values are not bounded then there is a deterministic protocol on anonymous systems using constant memory space that solves the same problem. Thus impossibility results on anonymous rings (i.e. one may design a deterministic SSLE protocol, only on prime size rings, under a centralized daemon) can be extended to those kinds of id-based rings. Nevertheless, it is possible to design a silent and deterministic SSLE protocol requiring constant memory space on unidirectional, id-based rings where the id-values are bounded. We present such a protocol. We also present a randomized SSLE protocol and a token circulation protocol under an unfair, distributed daemon on anonymous and unidirectional rings of any size. We give a lower bound on memory space requirement proving that these protocols are space optimal. The memory space required is constant on average. Keyword: self-stabilization, leader election, mutual exclusion, decidability, memory space requirement.

Randomized self-stabilizing and space optimal leader election under arbitrary scheduler on rings

We present a randomized self-stabilizing leader election protocol and a randomized self-stabilizing token circulation protocol under an arbitrary scheduler on anonymous and unidirectional rings of any size. These protocols are space optimal. We also give a formal and complete proof of these protocols. To this end, we develop a complete model for probabilistic self-stabilizing distributed systems which clearly separates the non deterministic behavior of the scheduler from the randomized behavior of the protocol. This framework includes all the necessary tools for proving the self- stabilization of a randomized distributed system: definition of a probabilistic space and definition of the self-stabilization of a randomized protocol. We also propose a new technique of scheduler management through a self-stabilizing protocol composition (cross-over composition). Roughly speaking, we force all computations to have a fairness property under any scheduler, even under an unfair one.

Anonymous publish/subscribe in P2P networks

One of the most important issues to deal with in peer-to-peer networks is how to disseminate information. In this paper, we use a completely new approach to solving the information dissemination problem. Our approach uses the publish/subscribe paradigm. The publish/subscribe method is the most inclusive strategy to establish communication between the information providers (publishers) and the information consumers (subscribers). We give a formal definition of publish/subscribe systems. We then use the publish/subscribe communication paradigm to design deterministic protocols (topic and content-based) for peer-to-peer networks. Our protocols are designed on top of an innovative information dissemination scheme, and can cope with the anonymity and mobility of both publishers and subscribers, weak-connectivity, and polarization, which are some of the characteristics of peer-to-peer networks. Moreover, in our solutions, every node could play a role of both publisher and subscriber The algorithms are designed completely independent of the underlying routing substrates. The key advantage of our protocols is that they are scalable without additional re-organization cost. To the best of our knowledge, this is the first time the content-based subscription has been addressed in peer-to-peer networks.

Conflict Managers for Self-stabilization without Fairness Assumption

In this paper, we specify the conflict manager abstraction. Informally, a conflict manager guarantees that any two nodes that are in conflict cannot enter their critical section simultaneously (safety), and that at least one node is able to execute its critical section (progress). The conflict manager problem is strictly weaker than the classical local mutual exclusion problem, where any node that requests to enter its critical section eventually does so (fairness). We argue that conflict managers are a useful mechanism to transform a large class of self-stabilizing algorithms that operate in an essentially sequential model, into self-stabilizing algorithm that operate in a completely asynchronous distributed model. We provide two implementations (one deterministic and one probabilistic) of our abstraction, and provide a composition mechanism to obtain a generic transformer. Our transformers have low overhead: the deterministic transformer requires one memory bit, and guarantees time overhead in order of the network degree, the probabilistic transformer does not require extra memory. While the probabilistic algorithm performs in anonymous networks, it only provides probabilistic stabilization guarantees. In contrast, the deterministic transformer requires initial symmetry breaking but preserves the original algorithm guarantees.

Publish/subscribe scheme for mobile networks

The information dissemination in mobile networks is an important but complex and challenging problem. Designing suitable communication primitives for these systems is critical. One of these primitives is the publish/subscribe paradigm. The publish/subscribe is a strategy to establish communication between the information providers (publishers) and information consumers (subscribers) in a distributed system. Our work focuses on an appropriate distributed infrastructure suitable for a scalable implementation of a publish/subscribe system. We present a formal model which is adapted for the peer-based particular subscription criteria of publish/subscribe systems. Moreover, we propose a general deterministic information diffusion scheme for mobile systems. The three main features of our communication scheme are the following: First, our scheme is well-adapted to scalable systems without compromising any subscription criteria or network reorganization. Second, we maintain the anonymity of the distributed system --- in order to maintain the network structure, we need only local information. Third, our solution is fully decentralized and modular, thus making it appropriate for practical implementations.

Incentives for P2P Fair Resource Sharing

We consider the problem of fair resource sharing to optimize the performance of resource sharing in peer to peer systems. Resource sharing systems currently face rational peers which may exhibit a variety of strategies including: no participation, also referred as free-riding, and greedy behavior. The first aspect has been extensively studied in the late years, while the second one has not received much attention. The broad class of proposed solutions focuses on designing incentives to reward cooperative peers. The side effect of these incentives is twofold: the system load is not balanced and the resource potential of the system is not fully exploited. The P2P fair resource sharing aims at both balancing the load and maximizing the use of system resources. The contribution of our work is twofold. First, we specify the P2P fair resource sharing problem and propose a mechanism to solve it in large scale dynamic networks with rational users. Our mechanism is composed of a novel incentive (i.e. fair cooperation) and an algorithmic part encapsulated in a middleware layer. Second, we propose an architecture for our mechanism middleware layer including four distributed services that bring together several research area: aggregation, semantic group membership and tracking. Finally, we implement our mechanism using a peer-to-peer unstructured model and evaluate it through simulations

Self-stabilizing Neighborhood Unique Naming under Unfair Scheduler

We propose a self-stabilizing probabilistic solution for the neighborhood unique naming problem in uniform, anonymous networks with arbitrary topology. This problem is important in the graph theory Our solution stabilizes under the unfair distributed scheduler. We prove that this solution needs in average only one trial per processor. We use our algorithm to transform the [6] maximal matching algorithm selfstabilizing to be able to cope up with a distributed scheduler.

Stabilizing Peer-to-Peer Spatial Filters

In this paper, we propose and prove correct a distributed stabilizing implementation of an overlay, called DR-tree, optimized for efficient selective dissemination of information. DR-tree copes with nodes dynamicity (frequent joins and leaves) and memory and counter program corruptions, that is, the processes can connect/disconnect at any time, and their memories and programs can be corrupted. The maintenance of the structure is local and requires no additional memory to guarantee its stabilization. The structure is balanced and is of height 0(logm(N)), which makes it suitable for performing efficient data storage or search. We extend our overlay in order to support complex content-based filtering in publish/subscribe systems. Publish/subscribe systems provide useful platforms for delivering data (events) from publishers to subscribers in a decoupled fashion in distributed networks. Developing efficient publish/subscribe schemes in dynamic distributed systems is still an open problem for complex subscriptions (spanning multi-dimensional intervals). Embedding a publish/subscribe system in a DR-trees is a new and viable solution. The DR-tree overlay also guarantees subscription and publication times logarithmic in the size of the network while keeping its space requirement low (comparable to its DHT-based counterparts). Nonetheless, the DR- tree overlay helps in eliminating the false negatives and drastically reduces the false positives in the embedded publish/subscribe system.