Bogosort

Abstract: : The paper asserts that the hidden-surface problem is mainly one of sorting. The various surfaces of an object to be shown in hidden-surface or hidden-line form must be sorted to find out which ones are visible at various places on the screen. Surfaces may be sorted by lateral position in the picture (XY), by depth (Z), or by other criteria. The paper shows that the order of sorting and the types of sorting used form differences among the existing hidden-surface algorithms. (Modified author abstract)

Abstract: The design and analysis of adaptive sorting algorithms has made important contributions to both theory and practice. The main contributions from the theoretical point of view are: the description of the complexity of a sorting algorithm not only in terms of the size of a problem instance but also in terms of the disorder of the given problem instance; the establishment of new relationships among measures of disorder; the introduction of new sorting algorithms that take advantage of the existing order in the input sequence; and, the proofs that several of the new sorting algorithms achieve maximal (optimal) adaptivity with respect to several measures of disorder. The main contributions from the practical point of view are: the demonstration that several algorithms currently in use are adaptive; and, the development of new algorithms, similar to currently used algorithms that perform competitively on random sequences and are significantly faster on nearly sorted sequences. In this survey, we present the basic notions and concepts of adaptive sorting and the state of the art of adaptive sorting algorithms.

Abstract: In this paper, we propose a taxonomy of parallel sorting that includes a broad range of array and file sorting algorithms. We analyze the evolution of research on parallel sorting, from the earliest sorting networks to the shared memory algorithms and the VLSI sorters. In the context of sorting networks, we describe two fundamental parallel merging schemes the odd-even and the bitonic merge. Sorting algorithms have been derived from these merging algorithms for parallel computers where processors communicate through interconnection networks such as the perfect shuffle, the mesh and a number of other sparse networks. After describing the network sorting algorithms, we show that, with a shared memory model of parallel computation, faster algorithms have been derived from parallel enumeration sorting schemes, where keys are first ranked and then rearranged according to their rank. Parallel sorting algorithms are evaluated according to a number of criteria, related not only to their time complexity, but also to their feasibility from a computer architecture point of view. We show that in addition to their attractive communication schemes, network sorting algorithms have non-adaptive schedules that make them suitable for implementation. In particular, they are easily generalized to block-sorting algorithms, that utilize limited parallelism to solve large sorting problems. We also address the problem of sorting large mass-storage files in parallel, using modified disk devices or intelligent bubble memories. Finally, the newer area of VLSI sorting is mentioned as an active and promising direction of research on parallel sorting.

Abstract: Analysis of genomes evolving by inversions leads to a general combinatorial problem of Sorting by Reversals, MIN-SBR, the problem of sorting a permutation by a minimum number of reversals. Following a series of preliminary results, Hannenhalli and Pevzner developed the first exact polynomial time algorithm for the problem of sorting signed permutations by reversals, and a polynomial time algorithm for a special case of unsigned permutations. The best known approximation algorithm for MIN-SBR, due to Christie, gives a performance ratio of 1.5. In this paper, by exploiting the polynomial time algorithm for sorting signed permutations and by developing a new approximation algorithm for maximum cycle decomposition of breakpoint graphs, we design a new 1.375-algorithm for the MIN-SBR problem.