Parallel Finger Search Structures In this paper we present two versions of a parallel finger structure FS on p processors that supports searches, insertions and deletions, and has a finger at each end. This is to our knowledge the first implementation of a parallel search structure that is workoptimal with respect to the finger bound and yet has very good parallelism (within a factor of O( (log p)2 ) of optimal). We utilize an extended implicit batching framework that transparently facilitates the use of FS by any parallel program P that is modelled by a dynamically generated DAG D where each node is either a unittime instruction or a call to FS.  :108,290,total work done by either version of FS is bounded by the finger bound FL (for some linearization L of D ), i.e. each operation on an item with finger distance r takes O( log r  1 ) amortized work; it is cheaper for items closer to a finger. Running P using the simpler version takes O( ( T1  FL )  p  Tinf  d * ( (log p)2  log n ) ) time on a greedy scheduler, where T1,Tinf are the size and span of D respectively, and n is the maximum number of items in FS, and d is the maximum number of calls to FS along any path in D. Using the faster version, this is reduced to O( ( T1  FL )  p  Tinf  d * (log p)2  sL ) time, where sL is the weighted span of D where each call to FS is weighted by its cost according to FL. We also sketch how to extend FS to support a fixed number of movable fingers.  data structures in our paper fit into the dynamic multithreading paradigm, and their performance bounds are directly composable with other data structures given in the same paradigm. Also, the results can be translated to practical implementations using workstealing schedulers.

NonBlocking Interpolation Search Trees with DoublyLogarithmic Running Time Most balanced search trees use key comparisons to guide their operations, and achieve logarithmic running time. By relying on numerical properties of the keys, interpolation search achieves lower search complexity and better performance. Although interpolationbased data structures were investigated in the past, their nonblocking concurrent variants have received very little attention so far.NIn this paper, we propose the first nonblocking implementation of the classic interpolation search tree data structure. For arbitrary key distributions, the data structure ensures amortized O(log n) insertion and deletion. Furthermore, when input key distributions are smooth, lookups run in expected O(log log n) time, and insertion and deletion run in amortized O(log log n). To improve the scalability of insertion and deletion operations, we propose a novel, scalable concurrent rebuilding technique. We implement the concurrent interpolation search tree, and evaluate the efficiency of its operations.NTrevor BrownUniversity