Commons Problems in Parallel Programming

Dining Philosophers Problem

140px-An_illustration_of_the_dining_philosophers_problemThis is a classic problem with data sharing and signaling.

Five (male) philosophers spend their lives thinking and eating. The philosophers share a common circular table surrounded by five chairs, each belonging to one philosopher. In the centre of the table there is a bowl of spaghetti, and the table is laid with five forks, as shown in figure. When a philosopher thinks, he does not interact with other philosophers. From time to time, a philosopher gets hungry. In order to eat he must try to pick up the two forks that are closest (and are shared with his left and right neighbors), but may only pick up one fork at a time. He cannot pick up a fork already held by a neighbor. When a hungry philosopher has both his forks at the same time, he eats without releasing them, and when he has finished eating, he puts down both forks and starts thinking again.

Solutions to this kind of problem are as follows:

  1. Use resource hierarchy: assign numbers to the forks (resources). The philosopher can only request resource with lower number first then the higher number.
  2. Use a central entity for assigning permissions: use a arbitrator (waiter) as a mutex which will allow the philosopher to periodically use the forks(resources).
  3. Distributed message passing between the philosophers without a central authority.
    1. For every pair of philosophers contending for a resource, create a fork and give it to the philosopher with the lower ID (n for agent Pn). Each fork can either be dirtyor clean. Initially, all forks are dirty.
    2. When a philosopher wants to use a set of resources (i.e. eat), said philosopher must obtain the forks from their contending neighbors. For all such forks the philosopher does not have, they send a request message.
    3. When a philosopher with a fork receives a request message, they keep the fork if it is clean, but give it up when it is dirty. If the philosopher sends the fork over, they clean the fork before doing so.
    4. After a philosopher is done eating, all their forks become dirty. If another philosopher had previously requested one of the forks, the philosopher that has just finished eating cleans the fork and sends it.

Sleeping Barber Problem

206px-Sleeping_barberThis is a classic single procedure multiple consumer problem.

The analogy is based upon a hypothetical barber shop with one barber. The barber has one barber chair and a waiting room with a number of chairs in it. When the barber finishes cutting a customer’s hair, they dismiss the customer and go to the waiting room to see if there are other customers waiting. If there are, they bring one of them back to the chair and cut their hair. If there are no other customers waiting, they return to their chair and sleep in it.

Each customer, when they arrive, looks to see what the barber is doing. If the barber is sleeping, the customer wakes them up and sits in the chair. If the barber is cutting hair, the customer goes to the waiting room. If there is a free chair in the waiting room, the customer sits in it and waits their turn. If there is no free chair, the customer leaves.

Author: Saurabh Purnaye

Sr. Developer @NYSE @ICE_Markets. Low Latency Trading, Linux, C++, Python, Ruby. pursuing certificate in #QuantFinance and Passed CFA L1

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