Skip lists: a probabilistic alternative to balanced trees

Communications of the ACM, June 1990

Skip lists are a data structure that can be used in place of balanced trees.

Skip lists use probabilistic balancing rather than strictly enforced balancing and as a result the algorithms for insertion and deletion in skip lists are much simpler and significantly faster than equivalent algorithms for balanced trees.

跳表是可以用于替代平衡树结构的一种更简单、易于实现的数据结构,RocksDB 用它实现 memtable。


跳表中的元素使用 Node 表示,每个 Node 都有对应的 Level,其值是在元素插入跳表时通过查询随机数生成器决定的。

random level

跳表的最大 Level 由其元素个数上限 N 决定,如果 p = 1/2,那么 MaxLevel = 16 的跳表可以容纳 2^16 个元素。

跳表的最后一个元素为 NIL,其 key 值大于任意元素的 key,任意 Level 的结尾都指向 NIL。

skip list

Search Algorithm

skip list search algorithm

Insertion Algorithm

skip list insertion algorithm


skip list insertion example

Deletion Algorithm

skip list deletion algorithm

p 值的选择

value of p

Since some of the constant overheads are related to L(n) (rather than L(n)/p), choosing p = 1/4 (rather than 1/2) slightly improves the constant factors of the speed of the algorithms as well.

I suggest that a value of 1/4 be used for p unless the variability of running times is a primary concern, in which case p should be 1/2.


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