Raymond's algorithm
# Raymond's algorithm

Raymond's Algorithm is a lock based algorithm for mutual exclusion on a distributed system. It imposes a logical structure (a K-ary tree) on distributed resources. As defined, each node has only a single parent, to which all requests to attain the token are made.

## Algorithm

### Nodal properties

* Each node has only one parent to whom received requests are forwarded
* Each node maintains a FIFO queue of requests each time that it sees the token;
* If any node is forwarding privilege to other node and has non-empty queue then it forwards a request message along

### Algorithm

* If a node i (not holding the token) wishes to receive the token in order to enter into its critical section, it sends a request to its parent, node j.
   * If node j FIFO is empty, node j shifts i into its FIFO queue; j then issues a request to its parent, k, that it desires the token
   * If node j FIFO queue is not empty, it simply shifts i into the queue
* When node k has token and receives the request from j it sends token to j and sets j as its parent
* When node j receives the token from k, it forwards the token to i and i is removed from the queue of j
   * If the queue of j is not empty after forwarding the token to i, j must issue a request to i in order to get the token back

Note: If j wishes to request a token, and its queue is not empty, then it places itself into its own queue. Node j will utilize the token to enter into its critical section if it is at the head of the queue when the token is received.

## Complexity

Raymond's algorithm is guaranteed to be O(log n) per critical section entry if the processors are organized into a K-ary tree. Additionally, each processor needs to store at most O(log n) bits because it must track O(1) neighbors.

