Rachid Hadid

A New Efficient Tool for the Design of Self-Stabilizing l-Exclusion Algorithms: The Controller

In this paper, we present the first self-stabilizing protocols for l-exclusion problem in the message passing model. The l-exclusion problem is a generalization of the mutual exclusion problem--we allow l (l ? 1) processors, instead of 1, to use a shared resource. We propose a new technique for the design of self-stabilizing l-exclusion: the controller. This tool allows to count tokens of the system without any counter variable for all processors except one called Root. We also introduce a new protocol composition called parametric composition. Then we present protocols on rings and on trees. The space requirement of both algorithms is independent of l for all processors except Root. The stabilization time of the first protocol is 3n time, where n is the ring size and the stabilization time of the second one is 6h + 2 time, where h is the tree height.

Space and Time Efficient Self-Stabilizing ℓ-Exclusion in Tree Networks

We propose an efficient self-stabilizing ?-exclusion algorithm in rooted tree networks running under an unfair distributed daemon. The ?-exclusion problem is a generalization of the mutual exclusion problem?? (??1) processors, instead of 1, are permitted to use a shared resource. The algorithm is semi-uniform and its space requirement is (?+3)?r states (or ?log((?+3)?r)? bits) for the root r, 4(?p?1) states (or ?2 log(?p?1)? bits) for an internal processor p, and 3 states (or 2 bits) for a leaf processor, where ?p is the degree of processor p. This is the first ?-exclusion algorithm on trees with the property that the space requirement is independent of the size of the network for any processor, and is independent of ? for all processors except the root. The stabilization time of the algorithm is only O(?+h) rounds, where h is the height of the tree.

A self‐stabilizing token‐based k‐out‐of‐ℓ exclusion algorithm

In this paper, we present the first self‐stabilizing solution to the k‐out‐of‐ℓ exclusion problem on a ring. The k‐out‐of‐ℓ exclusion problem is a generalization of the well‐known mutual exclusion problem—there are ℓ units of the shared resources, any process can request k

An adaptive stabilizing algorithm for finding all disjoint paths in anonymous mesh networks

(1 \leq k \leq \ell)

A new self-stabilizing k-out-of-l exclusion algorithm on rings

units of the shared resources, and no resource unit can be allocated to more than one process at one time. The space requirement of the proposed algorithm is independent of ℓ for all processors except a special processor, called Root. The stabilization time is only 5n, where n is the size of the ring. Copyright

A Self-stabilizing Token-Based k-out-of-l Exclusion Algorithm

In this paper, we present an adaptive stabilizing algorithm for finding all disjoint paths in anonymous mesh networks. Given two distinct nodes s and t of a network, the all disjoint paths problem is to identify all disjoint paths from s to t. Since our algorithm is stabilizing, it does not require initialization and withstands transient faults. In addition, the proposed algorithm adapts to topology changes in the form of process/link crashes and additions, i.e., upon a topology change, it finds all available paths from s to t. The space complexity of our algorithm is 4xd states for the source process s, one state for the target process, 120xd states for other processes, where d is the diameter of the communication network. The time complexity of the proposed algorithm is O(d) rounds. The proposed algorithm has a wide range of applications in ensuring reliability and security of sensor, mobile and fixed communication networks.

A Stabilizing Algorithm for Finding Two Node-Disjoint Paths in Arbitrary Networks

We present an efficient self-stabilizing solution to the k-out-of- l exclusion problem on a ring. The k-out-of-l exclusion problem is a generalization of the well-known mutual exclusion problem -- there are l units of a shared resource, any process can request at most k (1 ≤ k ≤ l) units of the shared resource, and no resource unit can be allocated to more than one process at one time. This solution is based on the circulation of l tokens around the ring. A processor requesting NEED (NEED ≤ k ≤ l) units of the resource can enter the critical section only upon receipt of NEED tokens. We propose a simple and pessimistic method to handle the deadlock problem. So, after stabilization, no mechanism is needed for the deadlock detection. Moreover, in this paper, we give a formal definition of a new efficiency property, called (k, l)-liveness, which is a desirable property of any k-out-of-l exclusion solution. This property allows as many processors as possible to execute their critical sections simultaneously without violating the safety property. We generalize the technique introduced in [6] to maintain the right number (l) tokens in the system. The tokens are counted without using any counter variable for all processors except one, called the Root. This solution improves the waiting time of an earlier solution [4] by maintaining a reasonable stabilization time. The waiting time is reduced from (l + 2)(n - 1) to 2(n - 1), where n is the size of the ring. The stabilization time is 8n instead of 4n in [4]. One nice characteristic of our algorithm is that its space requirement is independent of l for all processors except the Root.

A Stabilizing Optimal ℓ-Exclusion Algorithm

In this paper, we present the first self-stabilizing solution to the k out of l exclusion problem [14] on a ring. The k out of l exclusion problem is a generalization of the well-known mutual exclusion problem -- there are l units of the shared resources, any process can request some number k (1 ? k ? l) of units of the shared resources, and no resource unit is allocated to more than one process at one time. The space requirement of the proposed algorithm is independent of l for all processors except a special processor, called Root. The stabilization time of the algorithm is only 5n, where n is the size of the ring.

A Self-Stabilizing Algorithm for the Generalization of the Mutual Exclusion Problem

The problem of two node-disjoint paths is to identify two paths 𝒬1 and 𝒬2 from source s ∈ V to target t ∈ V without any common intermediate node in a communication network G = (V,E), where each nod...

An optimal snap-stabilizing wave algorithm in arbitrary graphs

In this paper, we present a simple permission-based fair stabilizing solution to the l-exclusion problem in tree networks. The l-exclusion problem is a generalization of the mutual exclusion problem where l>1 processes, instead of 1, are allowed to use a shared resource (enter the critical section) simultaneously. The proposed algorithm is optimal in terms of waiting times of processes to enter critical sections, i.e., between two entries of a process to its critical section, no other process can enter its critical section more than once after stabilization. Since our algorithm is stabilizing, it does not require initialization and withstands transient faults. The stabilization time of the algorithm is 3×h+6 rounds and the waiting time is (n−1), where h and n are the height and the size of the tree, respectively. In addition, this algorithm satisfies all the requirements of the l-exclusion problem: safety,fairness, and liveness.