Towards Provably Scalable Concurrent Search Algorithms

This report contains complementary definitions on sequential proximity [2]. Furthermore, in this report we motivate sequential proximity by using it to prove that two concurrent search data structures are sequentially proximal and show how sequentially proximity can help a developer create a highly-scalable linked list. In Section 2 we present related work. In Section 3 we give precise definitions for logical deletion and cleaning-up stores. Then, in Section 4 we prove two relations between sequential proximity properties and classic progress conditions. In Section 5 we prove that a lock-based linked list [17] is sequentially proximal, while in Section 6 we prove that a non-blocking linked list [16] satisfies sequential proximity. We conclude in Section 7 where we present the trend of concurrent search data structures towards sequential proximity, an example on how we can end-up with a highly-scalable concurrent linked list and some instances where sequential proximity is violated.