Maekawa's algorithm
# Maekawa's algorithm

Maekawa's algorithm is an algorithm for mutual exclusion on a distributed system. The basis of this algorithm is a quorum-like approach where any one site needs only to seek permissions from a subset of other sites.

## Algorithm

### Terminology

* A site is any computing device which runs the Maekawa's algorithm
* For any one request of entering the critical section:
   * The requesting site is the site which is requesting to enter the critical section.
   * The receiving site is every other site which is receiving the request from the requesting site.
* ts refers to the local time stamp of the system according to its logical clock

### Algorithm

Requesting site:

* A requesting site $P_{i}$ sends a message ${\text{request}}(ts,i)$ to all sites in its quorum set $R_{i}$.

Receiving site:

* Upon reception of a ${\text{request}}(ts,i)$ message, the receiving site $P_{j}$ will:
   * If site $P_{j}$ does not have an outstanding ${\text{grant}}$ message (that is, a ${\text{grant}}$ message that has not been released), then site $P_{j}$ sends a ${\text{grant}}(j)$ message to site $P_{i}$.
   * If site $P_{j}$ has an outstanding ${\text{grant}}$ message with a process with higher priority than the request, then site $P_{j}$ sends a ${\text{failed}}(j)$ message to site $P_{i}$ and site $P_{j}$ queues the request from site $P_{i}$.
   * If site $P_{j}$ has an outstanding ${\text{grant}}$ message with a process with lower priority than the request, then site $P_{j}$ sends an ${\text{inquire}}(j)$ message to the process which has currently been granted access to the critical section by site $P_{j}$. (That is, the site with the outstanding ${\text{grant}}$ message.)
* Upon reception of a ${\text{inquire}}(j)$ message, the site $P_{k}$ will:
   * Send a ${\text{yield}}(k)$ message to site $P_{j}$ if and only if site $P_{k}$ has received a ${\text{failed}}$ message from some other site or if $P_{k}$ has sent a yield to some other site but have not received a new ${\text{grant}}$.
* Upon reception of a ${\text{yield}}(k)$ message, site $P_{j}$ will:
   * Send a ${\text{grant}}(j)$ message to the request on the top of its own request queue. Note that the requests at the top are the highest priority.
   * Place $P_{k}$ into its request queue.
* Upon reception of a ${\text{release}}(i)$ message, site $P_{j}$ will:
   * Delete $P_{i}$ from its request queue.
   * Send a ${\text{grant}}(j)$ message to the request on the top of its request queue.

Critical section:

* Site $P_{i}$ enters the critical section on receiving a ${\text{grant}}$ message from all sites in $R_{i}$.
* Upon exiting the critical section, $P_{i}$ sends a ${\text{release}}(i)$ message to all sites in $R_{i}$.

Quorum set ($R_{x}$): A quorum set must abide by the following properties:

* $\forall i\,\forall j\,[R_{i}\bigcap R_{j}\neq \emptyset ]$
* $\forall i\,[P_{i}\in R_{i}]$
* $\forall i\,[|R_{i}|=K]$
* Site $P_{i}$ is contained in exactly $K$ request sets

    Therefore:
   * $|R_{i}|\geq {\sqrt {N-1}}$

### Performance

* Number of network messages; $3{\sqrt {N}}$ to $6{\sqrt {N}}$
* Synchronization delay: 2 message propagation delays
* The algorithm can deadlock without protections in place.
