Finding succinct ordered minimal perfect hashing functions

An ordered minimal perfect hash table is one in which no collisions occur among a predefined set of keys, no space is unused, and the data are placed in the table in order. A new method for creating ordered minimal perfect hashing functions is presented. The method presented is based on a method developed by Fox, Heath, Daoud, and Chen, but it creates hash functions with representation space requirements closer to the theoretical lower bound. The method presented requires approximately 10% less space to represent generated hash functions, and is easier to implement than Fox et al's. However, a higher time complexity makes it practical for small sets only (< 1000)

Lower bounds for the stable marriage problem and its variants

In an instance of the stable marriage problem of size n, n men and n women each ranks members of the opposite sex in order of preference. A stable marriage is a complete matching M = {(m_1, w_i_1), (m_2, w_i_2), ..., (m_n, w_i_n)} such that no unmatched man and woman prefer each other to their partners in M.A pair (m_i, w_j) is stable if it is contained in some stable marriage. In this paper, we prove that determining if an arbitrary pair is stable requires Ω(n^2) time in the worst case. We show, by an adversary argument, that there exists instances of the stable marriage problem such that it is possible to find at least one pair that exhibits the Ω(n^2) lower bound.As corollaries of our results, the lower bound of Ω(n^2) is established for several stable marriage related problems. Knuth, in his treatise on stable marriage, asks if there is an algorithm that finds a stable marriage in less than Θ(n^2) time. Our results show that such an algorithm does not exist

Complexity of the stable marriage and stable roommate problems in three dimensions

The stable marriage problem is a matching problem that pairs members of two sets. The objective is to achieve a matching that satisfies all participants based on their preferences. The stable roommate problem is a variant involving only one set, which is partitioned into pairs with a similar objective. There exist asymptotically optimal algorithms that solve both problems.In this paper, we investigate the complexity of three dimensional extensions of these problems. This is one of twelve research directions suggested by Knuth in his book on the stable marriage problem. We show that these problems are NP-complete, and hence it is unlikely that there exist efficient algorithms for their solutions.Applying the polynomial tranformation developed in this paper, we extend the NP-completeness result to include the problem of matching couples - who are both medical school graduates - to pairs of hospital resident positions. This problem is important in practice and is dealth with annually by NRMP, the centralized program that matches all medical school graduates in the United States to available resident positions

Tools for efficient analysis of concurrent software systems

The ever increasing use of distributed computing as a method of providing added computing power and reliability has sparked interest in methods to model and analyze concurrent hardware/ software systems. Efficient automated analysis tools are needed to aid designers of such systems. The Distributed Systems Project at UCI has been developing a suite of tools (dubbed the P-NUT system) which supports efficient analysis of models of concurrent software. This paper presents the principles which guide the development of P-NUT tools and discusses the development of one of the tools: the Reachability Graph Builder (RGB). The P-NUT approach to tool development has resulted in the production of a highly efficient tool for constructing reachability graphs. The careful design of data structures and associated algorithms has significantly enlarged the class of models which can be analyzed

Self-organizing lists on the Xnet

The first parallel designs for implementing self-organizing lists on the Xnet interconnection network are presented. Self-organizing lists permute the order of list entries after an entry is accessed according to some update hueristic. The heuristic attempts to place frequently requested entries closer to the front of the list. This paper outlines Xnet systems for self-organizing lists under the move-to-front and transpose update heuristics. Our novel designs can be used to achieve high-speed lossless text compression

Parallel data compression

Data compression schemes remove data redundancy in communicated and stored data and increase the effective capacities of communication and storage devices. Parallel algorithms and implementations for textual data compression are surveyed. Related concepts from parallel computation and information theory are briefly discussed. Static and dynamic methods for codeword construction and transmission on various models of parallel computation are described. Included are parallel methods which boost system speed by coding data concurrently, and approaches which employ multiple compression techniques to improve compression ratios. Theoretical and empirical comparisons are reported and areas for future research are suggested

Improved Combinatorial Group Testing Algorithms for Real-World Problem Sizes

We study practically efficient methods for performing combinatorial group testing. We present efficient non-adaptive and two-stage combinatorial group testing algorithms, which identify the at most d items out of a given set of n items that are defective, using fewer tests for all practical set sizes. For example, our two-stage algorithm matches the information theoretic lower bound for the number of tests in a combinatorial group testing regimen.Comment: 18 pages; an abbreviated version of this paper is to appear at the 9th Worksh. Algorithms and Data Structure

Improved Adaptive Group Testing Algorithms with Applications to Multiple Access Channels and Dead Sensor Diagnosis

We study group-testing algorithms for resolving broadcast conflicts on a multiple access channel (MAC) and for identifying the dead sensors in a mobile ad hoc wireless network. In group-testing algorithms, we are asked to identify all the defective items in a set of items when we can test arbitrary subsets of items. In the standard group-testing problem, the result of a test is binary--the tested subset either contains defective items or not. In the more generalized versions we study in this paper, the result of each test is non-binary. For example, it may indicate whether the number of defective items contained in the tested subset is zero, one, or at least two. We give adaptive algorithms that are provably more efficient than previous group testing algorithms. We also show how our algorithms can be applied to solve conflict resolution on a MAC and dead sensor diagnosis. Dead sensor diagnosis poses an interesting challenge compared to MAC resolution, because dead sensors are not locally detectable, nor are they themselves active participants.Comment: Expanded version of a paper appearing in ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), and preliminary version of paper appearing in Journal of Combinatorial Optimizatio