0%

Notes of Non-blocking Binary Search Trees

specification

  • no duplicate key

  • deleting non-existent key leads to return false

  • leaf-oriented BST

    • all keys currently in the dictionary are stored in the leaves of the tree.
    • Internal nodes of the tree are used to direct a Find operation along the path to the correct leaf.
    • The keys stored in internal nodes may or may
      not be in the dictionary.

features

  • non-blocking

  • linearizable

    for every execution, one can assign a linearization point to each completed operation and some of the uncompleted operations so that the linearization point of each operation occurs after the operation starts and before it ends, and the results of these operations are the same as if they had been performed sequentially, in the order of their linearization points.

basic idea

类似Harris’ Linked List里面的做法,这里是mark the parent of the leaf before
splicing that parent out of the tree。一旦被标记,那么其指向子结点的指针将不能被改变。

problems

上图中,两个线程分别delete C和E,两个concurrent operation同时看到了BST以后,接下来的操作是,基于各自看到的的BST来进行的,它们彼此并不知道对方进行了什么操作,最后导致E并没有被deleted,其中一个操作丢失了。

解决这个需要对parent的child pointer进行mark,但是要mark的pointer是存在两个不同的word(left and right child pointer)里面的,不能够用一个cas来同时mark。

solutions

using a separate state field of the node to mark or flag,而不是mark那个pointer。

  • mark: node marked is unchangeable。
  • flag: indicate that an update is trying to change a child pointer of the node.

mark和flag类似于加锁。

insert和delete

insert

Insert (C):

  1. flag node D’s parent, node B,
  2. change the appropriate child pointer of node B,
  3. unflag node B.

delete

Delete (C):

  1. flag C’s grandparent, node B,
  2. mark C’s parent, node D,
  3. change the appropriate child pointer of B,
  4. unflag node B.

insert在完成第一步以后,在insert进行后续操作时,其他线程将不能够block insert。delete类似的,在完成第一二步以后也是。

但是delete在完成第一步以后,第二步mark有可能失败,比如insert把将要删除的node换为新的三个node。in which case the flag is no longer on the node whose child pointer must be changed to accomplish the deletion.

如果mark失败,delete会remove flag,重新开始。

some details in implementation

helping mechanism

method

类似Barnes的方法,将线程拥有lock换成操作拥有lock(marked or flagged)。一个操作在处理tree的同时,还保存了它在holding lock的时候要进行的操作,其他线程遇到lock,就帮助它完成,使得lock最终release。

为了避免helping mechanism带来的性能下降(多个线程会尝试进行同一个操作),这里用了保守的策略: a process P helps another process’s operation only if the other operation is preventing P’s own progress.

implementation

线程之间是无法自动感知对方的存在的,也就是说实现helping mechanism,需要a data structure that is shared between threads holds the operating information。

dummy keys

在delete时,需要flag grandparent和mark parent,如果BST的key少于4个,必然就会有一个leaf没有grandparent,那么在delete就需要考虑很多例外的情况(insert类似)。

为了避免这些特殊情况,下面引入两个特殊值$\infty_1$和$\infty_2$,使得BST在没有key的时候,也存在3个node。这两个dummy keys是不允许删除的。

summary

  1. Excellent tutorial about helping mechanism!!!
  2. 在树上面进行并发操作的时候,这篇论文中描述的问题其实大都是存在的,因此论文中的方法可以考虑用到其他树型结构上面。

references

  1. Non-blocking Binary Search Trees, Faith Ellen, Panagiota Fatourou, Eric Ruppert, Franck van Breugel