We settle the question of tight thresholds for offline cuckoo hashing. The problem can be stated as follows: we have n keys to be hashed into m buckets each capable of holding a single key. Each key has k ≥ 3 (distinct) associated buckets chosen uniformly at random and independently of the choices of other keys. A hash table can be constructed successfully if each key can be placed into one of its buckets. We seek thresholds ck such that, as n goes to infinity, if n/m ≤ c for some c < ck then a hash table can be constructed successfully with high probability, and if n/m ≥ c for some c> ck a hash table cannot be constructed successfully with high probability. Here we are considering the offline version of the problem, where all keys and hash values are given, so the problem is equivalent to previous models of multiple-choice hashing. We find the thresholds for all values of k> 2 by showing that they are in fact the same as the previously known thresholds for the random k-XORSAT problem. We then extend these results to the setting where keys can have differing number of choices, and provide evidence in the form of an algorithm for a conjecture extending this result to cuckoo hash tables that store multiple keys in a bucket.

We present FlashStore, a high throughput persistent keyvalue store, that uses flash memory as a non-volatile cache between RAM and hard disk. FlashStore is designed to store the working set of key-value pairs on flash and use one flash read per key lookup. As the working set changes over time, space is made for the current working set by destaging recently unused key-value pairs to hard disk and recycling pages in the flash store. FlashStore organizes key-value pairs in a log-structure on flash to exploit faster sequential writeperformance. Itusesanin-memoryhashtabletoindex them, with hash collisions resolved by a variant of cuckoo hashing. The in-memory hash table stores compact key signatures instead of full keys so as to strike tradeoffs between RAM usage and false flash read operations. FlashStore can be used as a high throughput persistent key-value storage layer for a broad range of server class applications. We compare FlashStore with BerkeleyDB, an embedded key-value store application, running on hard disk and flash separately, so as to bring out the performance gain of FlashStore in not only using flash as a cache above hard disk but also in its use of flash aware algorithms. We use real-world data traces from two data center applications, namely, Xbox LIVE Primetime online multi-player game and inline storage deduplication, to drive and evaluate the design of FlashStore on traditional and low power server platforms. FlashStore outperforms BerkeleyDB by up to 60x on throughput (ops/sec), up to 50x on energy efficiency (ops/Joule), and up to 85x on cost efficiency (ops/sec/dollar) on the evaluated datasets. 1.

Abstract. CHR is usually compiled to high-level languages (like Prolog) that make it hard or impossible to express low-level optimizations. This is a pity, because it confines CHR to be a prototyping language only, with an unacceptable performance for production quality software. This paper presents CCHR, a CHR system embedded in the C programming language, that compiles to low-level C code which is highly suitable for fine-grained performance improvements. In this way CCHR program performance comes close to matching that of native C, and easily outperforms other CHR implementations. 1

SILT (Small Index Large Table) is a memory-efficient, high-performance key-value store system based on flash storage that scales to serve billions of key-value items on a single node. It requires only 0.7 bytes of DRAM per entry and retrieves key/value pairs using on average 1.01 flash reads each. SILT combines new algorithmic and systems techniques to balance the use of memory, storage, and computation. Our contributions include: (1) the design of three basic key-value stores each with a different emphasis on memory-efficiency and write-friendliness; (2) synthesis of the basic key-value stores to build a SILT key-value store system; and (3) an analytical model for tuning system parameters carefully to meet the needs of different workloads. SILT requires one to two orders of magnitude less memory to provide comparable throughput to current high-performance key-value systems on a commodity desktop system with flash storage.

We present a strongly history independent (SHI) hash table that supports search in O(1) worst-case time, and insert and delete in O(1) expected time using O(n) data space. This matches the bounds for dynamic perfect hashing, and improves on the best previous results by Naor and Teague on history independent hashing, which were either weakly history independent, or only supported insertion and search (no delete) each in O(1) expected time. The results can be used to construct many other SHI data structures. We show straightforward constructions for SHI ordered dictionaries: for n keys from {1,..., n k} searches take O(log log n) worst-case time and updates (insertions and deletions) O(log log n) expected time, and for keys in the comparison model searches take O(log n) worst-case time and updates O(log n) expected time. We also describe a SHI data structure for the order-maintenance problem. It supports comparisons in O(1) worst-case time, and updates in O(1) expected time. All structures use O(n) data space. 1

Abstract Hashing is an extremely useful technique for a variety of high-speed packet-processing applications in routers. In this chapter, we survey much of the recent work in this area, paying particular attention to the interaction between theoretical and applied research. We assume very little background in either the theory or applications of hashing, reviewing the fundamentals as necessary. 1

Database storage managers have long been able to efficiently handle multiple concurrent requests. Until recently, however, a computer contained only a few single-core CPUs, and therefore only a few transactions could simultaneously access the storage manager's internal structures. This allowed storage managers to use non-scalable approaches without any penalty. With the arrival of multicore chips, however, this situation is rapidly changing. More and more threads can run in parallel, stressing the internal scalability of the storage manager. Systems optimized for high performance at a limited number of cores are not assured similarly high performance at a higher core count, because unanticipated scalability obstacles arise. We benchmark four popular open-source storage managers (Shore, BerkeleyDB, MySQL, and PostgreSQL) on a modern multicore machine, and find that they all suffer in terms of scalability. We briefly examine the bottlenecks in the various storage engines. We then present Shore-MT, a multithreaded and highly scalable version of Shore which we developed by identifying and successively removing internal bottlenecks. When compared to other DBMS, Shore-MT exhibits superior scalability and 2-4 times higher absolute throughput than its peers. We also show that designers should favor scalability to single-thread performance, and highlight important principles for writing scalable storage engines, illustrated with real examples from the development of Shore-MT.

We consider the online stochastic matching problem proposed by Feldman et al. [4] as a model of display ad allocation. We are given a bipartite graph; one side of the graph corresponds to a fixed set of bins and the other side represents the set of possible ball types. At each time step, a ball is sampled independently from the given distribution and it needs to be matched upon its arrival to an empty bin. The goal is to maximize the size of the matching. We present an online algorithm for this problem with a competitive ratio of 0.702. Before our result, algorithms with a competitive ratio better than 1 − 1/e were known under the assumption that the expected number of arriving balls of each type is integral. A key idea of the algorithm is to collect statistics about the decisions of the optimum offline solution using Monte Carlo sampling and use those statistics to guide the decisions of the online algorithm. We also show that no online algorithm can have a competitive ratio better than 0.823. 1

Bucketized versions of Cuckoo hashing can achieve 95– 99 % occupancy, without any space overhead for pointers or other structures. However, such methods typically need to consult multiple hash buckets per probe, and have therefore been seen as having worse probe performance than conventional techniques for large tables. We consider workloads typical of database and stream processing, in which keys and payloads are small, and in which a large number of probes are processed in bulk. We show how to improve probe performance by (a) eliminating branch instructions from the probe code, enabling better scheduling and latency-hiding by modern processors, and (b) using SIMD instructions to process multiple keys/payloads in parallel. We show that on modern architectures, probes to a bucketized Cuckoo hash table can be processed much faster than conventional hash table probes, for both small and large memory-resident tables. On a Pentium 4, a probe is two to four times faster, while on the Cell SPE processor a probe is ten times faster. 1

Cuckoo hashing is an efficient and practical dynamic dictionary. It provides expected amortized constant update time, worst case constant lookup time, and good memory utilization. Various experiments demonstrated that cuckoo hashing is highly suitable for modern computer architectures and distributed settings, and offers significant improvements compared to other schemes. In this work we construct a practical history-independent dynamic dictionary based on cuckoo hashing. In a history-independent data structure, the memory representation at any point in time yields no information on the specific sequence of insertions and deletions that led to its current content, other than the content itself. Such a property is significant when preventing unintended leakage of information, and was also found useful in several algorithmic settings. Our construction enjoys most of the attractive properties of cuckoo hashing. In particular, no dynamic memory allocation is required, updates are performed in expected amortized constant time, and membership queries are performed in worst case constant time. Moreover, with high probability, the lookup procedure queries only two memory entries which are independent and can be queried in parallel. The approach underlying our construction is to enforce a canonical memory representation on cuckoo hashing. That is, up to the initial randomness, each set of elements has a unique memory representation.