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                    Mahmoud H.M. — Sorting: a distribution theory 
                  
                
                    
                        
                            
                                
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                                    Íàçâàíèå:   Sorting: a distribution theory 
Àâòîð:   Mahmoud H.M.   
Àííîòàöèÿ:  A cutting-edge look at the emerging distributional theory of sorting
 
 Research on distributions associated with sorting algorithms has grown dramatically over the last few decades, spawning many exact and limiting distributions of complexity measures for many sorting algorithms. Yet much of this information has been scattered in disparate and highly specialized sources throughout the literature. In Sorting: A Distribution Theory, leading authority Hosam Mahmoud compiles, consolidates, and clarifies the large volume of available research, providing a much-needed, comprehensive treatment of the entire emerging distributional theory of sorting.
 
 Mahmoud carefully constructs a logical framework for the analysis of all standard sorting algorithms, focusing on the development of the probability distributions associated with the algorithms, as well as other issues in probability theory such as measures of concentration and rates of convergence. With an emphasis on narrative rather than technical explanations, this exceptionally well-written book makes new results easily accessible to a broad spectrum of readers, including computer professionals, scientists, mathematicians, and engineers. Sorting: A Distribution Theory:
 * Contains introductory material on complete and partial sorting
 * Explains insertion sort, quick sort, and merge sort, among other methods
 * Offers verbal descriptions of the mechanics of the algorithms as well as the necessary code
 * Illustrates the distribution theory of sorting using a broad array of both classical and modern techniques
 * Features a variety of end-of-chapter exercises
 
ßçûê:   
Ðóáðèêà:  Computer science /Àëãîðèòìû / 
Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ:  Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö  
ed2k:   ed2k stats  
Ãîä èçäàíèÿ:  2000 
Êîëè÷åñòâî ñòðàíèö:  396 
Äîáàâëåíà â êàòàëîã:  19.11.2005 
Îïåðàöèè:  Ïîëîæèòü íà ïîëêó  |
	 
	Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà  | Ñêîïèðîâàòü ID 
                                 
                             
                        
                     
                 
                                                                
			         
	          
                
                    Ïðåäìåòíûé óêàçàòåëü 
                  
                
                    
                        Adversary        26   27   36   126    
Adversary argument        26—29   36    
Aldous, D.        62    
Alternating sum        75    
Analytic continuation        62   99    
Andrews, D.        3    
Arratia, R.        62    
ASCII        90    
Asymptotic integration        55    
Australian median-of-three algorithm        205    
Barbour, A.        161    
Base function        57    
Base of number system        260; see “Radix”    
Bent, S.        30    
Berry — Esseen bound        92   94    
beta function        75   114    
Bickel, P.        3    
Binary search        83—84   95   101—102   227   230   287    
Bit        260    
Blum, M.        25   294   297    
Brown, R.        107    
Brownian bridge        109   103   106—112    
Brownian bridge, absolute        112    
Brownian bridge, standard        109    
Brownian motion        109   106—108    
Brownian motion, incremental        107—109    
Bubble sort        129—131    
Bubble sort, pass of        129    
Bucket sorting        250    
Bucket sorting, principle of        250    
Bucketing        251    
Bucketing, digital        259    
Carlsson, S.        219    
Carroll, L.        26    
Cartesian product        7    
Cauchy — Riemann conditions        55    
Cauchy — Saalschuetz Gamma function        59    
Cauchy’s residue theorem        55   58   64   74—76   257    
Chambers        166   177    
Chao, C.        50    
Chebyshev’s inequality        51   136   196    
Chernoff, H.        196    
Closing the box method        58    
Coefficient transfer        279    
Collating sequence        90    
Comparable elements        7    
Constant phase path        55    
Continuity theorem        369    
Contraction mapping        159    
Convolution        121   167   188   239   268—269   301    
Cramer, M.        242    
Cumulants        159    
Curran, J.        128    
CYCLE        43   46    
Cycle representation        46   47—48    
Cycle representation, canonical        46   47—48    
de Bruijn, N.        135   264    
De-Poissonization        61    
De-Poissonization, cone of        63    
De-Poissonization, lemma        64   265    
Delange, H.        81   247   249    
Demuth, H.        25    
Devroye, L.        18    
Difference, backward        70    
Difference, forward        70    
Difference, martingale        51    
Dirichlet generating function        70    
Dirichlet transform        see “Transform”    
Disorder        284    
Distributive selection        270—271   273    
Distributive sort        251    
Divide and conquer        5   220   148   304    
DNA        260—261    
Doberkat, E.        94    
Dobosiewicz, W.        138   250   256   281    
Dor, D.        25   30—31    
Einstein, A.        107    
Empirical distribution function        106   112—113    
Esseen, X.        see “Berry — Esseen bound”    
Euler’s constant        61   264    
Euler’s differential equation        202    
External path length        13    
Fibonacci search        86    
Fixed point        159    
Flajolet, P.        70   73   235   238   242   244   247   256   266   268   274   279—280    
Floyd, R.        25   212   214   216—219   294   297    
Foata, D.        43   47    
Ford — Johnson algorithm        286—289   291—293    
Fourier expansion        235   238   264    
Fourier transform        see “Transform”    
Fractal        247    
Frank, R.        124    
Frazer, W.        207—209    
Frobenius Number        124   126—128    
Gamma function        60   266    
Gamma function method        264 (see also “Closing the box method”)    
Gastwirth, J.        3    
Gaussian law        86—87   100—102   115   300    
Generator sequence        124   125   127    
Geometrization        61    
Golin, M.        70   73   235   238   242   244   247    
Goncharov, V.        43   48    
Gonnet, G.        62—63   219   253—254    
Grabner, P.        61    
Grand average        167    
Grand distribution        167—168    
Grand variance        167    
Gries, D.        83—84   87    
Hadian, A.        291    
Hadjicostas, P.        159    
Hampel, F.        3    
Harmonic number        42   368    
Harmonic sum        57   59    
Hash function        251   281   283    
Hash table        250    
Hashing        250   272   283   305    
Hashing with linear probing        84    
Hayward, R.        159    
Heap        213   212    
Heap construction        214—217    
Heap sorting        217—218    
Heap, conceptual        213    
Hennequin, P.        159    
Hibbard, T.        124    
Hoare, C.        148   155   166—167   170   172   177   208   294    
Holst, L.        62   161    
Huber, P.        3    
Hunt, D.        123    
Hwang — Lin merging algorithm        221   228—230   293    
Hwang, F.        see “Hwang — Lin merging algorithm”    
Hwang, H.        81   298—300   302    
Incerpi, J.        124    
Incomparable elements        7    
Indegree        11    
Infinitely divisible distribution        175   167   176—177    
Information theory        23    
Insertion sort        83—84    
Insertion sort, binary        95    
Insertion sort, jump        101    
Insertion sort, linear        88—94   103—105   119    
Insertion sort, randomized        102    
Internal path length        13    
Interpolation select        271—274   282    
Interpolation sort        253—255    
inversion        44   45—46   91   127   132   284   299—301    
Jacobian        110    
Jacquet, P.        62   64   81   256   266   268   274   280    
Janson, S.        161    
John, J.        30    
Johnson, B.        113    
Johnson, S.        see “Ford — Johnson algorithm”    
Kac, M.        61    
Key        4    
Killeen, T.        113    
Kirschenhofer, P.        172   205    
Kislitsyn, S.        29   33   35    
Knuth, D.        23   118—119   123   125   133   135   157   170   209   264   289   292    
Kolmogorov’s canonical representation        177    
Landau, L.        367    
Laplace, P.        see “Transform”    
Law of Large Numbers        51   136   369    
Law of Large Numbers, strong        106—107   369    
Lazarus, R.        124    
Lebesgue measure        159    
Lebesgue — Stieltjes integration        46    
Lent, J.        15   87   182   187   196    
Lin, S.        see “Hwang — Lin merging algorithm”    
Lindeberg’s central limit theorem        88    
Lindeberg’s condition        43   45   88   370   371    
Lindeberg’s conditional        51   372    
Linear search        86    
Linear search, backward        86    
Linear search, forward        86    
Louchard, G.        118   121    
Lyapunov’s condition        242—243   377    
Mahmoud, H.        15   43   87   166   172—174   176   182   187   190   195—196   256   264   266   268   274   280   289   292    
Manacher, G.        286   293    
Mannila, H.        302    
Maple        156    
Martinez, C.        205   372    
Martingale        49—52   372    
Martingale central limit theorem        50—52   372    
Martingale convergence theorem        158   372    
Martingale difference        51   372    
Martingale transform        50    
Martingale, conditional variance in        51—52   372    
Martingalization        49—50    
Master Mind        27—29    
Mathematica        156    
McDiarmid, C.        159    
McKellar, A.        207—209    
Mellin — Perron formula        67    
Mellin, H.        see “Transform”    
Melville, R.        83—84   87    
Merge sort        220—222    
Merge sort, bottom-up        243—245    
Merge sort, top-down        220    
Merging, binary        227—228   230   293    
Merging, Hwang — Lin        228—230    
Merging, linear        222—224    
Meyer, R.        36    
Modarres, R.        166   172—174   176   195—196    
Moment generating function        53    
Moment generating function, bivariate        54    
Moment generating function, super        54   261—262    
MQS tree        178    
Munro, I.        62—63   219    
Object-Oriented Programming        309    
Odlyzko, A.        279    
Oracle        27    
Order        7    
Order statistic        1    
Order statistic, median        3    
Order statistic, quantile        3    
Order statistic, quartile        3    
Order statistic, tertile        3    
Order, partial        7    
Order, total        7    
Outdegree        11    
Outlier        178    
Panholzer, A.        190—191    
Panny, W.        94   244   247—248    
Papernov, A.        124   128    
Partial order        7    
Partial order, chain of        8    
Partial order, induced        20    
Partially ordered set        7    
Pascal, programming language        86   90    
Pascal’s identity        240    
Paterson, M.        25    
Path of maximal sons        216   218—219    
Permutation        2    
Permutation, random        15   37   105   150—151   206   225   255   283   301    
Perron, O.        see “Mellin — Perron formula”    
Pippenger, N.        25    
Pivot        149    
Plaxton, C.        124    
Poblete, P.        62   256    
Pochhammer’s symbol        181    
Poisson compound law        275    
Poissonization        61   263    
Poissonized average        264—265    
Poissonized cost        263    
Poonen, B.        124   127    
POSET        7    
Pratt, V.        25   125   127   294   297    
Presortedness        284    
Presortedness, measure of        284    
Presorting        298    
Probability integral transform        112   117    
Probe sequence        85   95    
Prodinger, H.        172   180   182   190—191   205   244   247—248    
Pseudocode        6    
Quantile scheme        206   211    
Query        18    
Quick sort tree        152   178    
RADIX        260    
Radix sort        259—261    
Radix, binary        260    
Radix, decimal        260    
Radix, hexadecimal        260    
Radix, octal        260    
Rais, B.        62   81    
Ramanujan, S.        135    
random number generation        285    
Random number generation, pseudo-        285    
Random walk        107    
Random walk, symmetric        107    
Randomization        285    
Randomized QUICK SORT        285    
Rank        37    
Rank, absolute        37    
Rank, sequential        37    
Rate of convergence        86   266    
Rayleigh distribution        133    
Record        41—43   46—48   141    
Regnier, M.        62   157   256   266   268   274   280    
Relation        7    
Relation from        7    
Relation on        7    
Relation, antisymmetric        7    
Relation, reflexive        7    
Relation, transitive        7    
Rice method        75   74—76    
Rice, S.        74    
Riemann, B.        see “Cauchy — Riemann conditions”    
Rivest, R.        25   294   297    
Roesler, U.        159   164   168   194   204    
Rogers, W.        3    
Run        48   49—52   284    
Saalschuetz, L.        see “Cauchy — Saalschuetz Gamma function”    
Saddle point        55   64   67   257   281    
Saddle point method        257    
Schaffer, R.        219    
Schoenhage, A.        25    
Schreier, J.        34—35    
Search strategy        84    
Sedgewick, R.        124   170   194   204   219   259    
Selection        2    
Selection, fixed        166    
                            
                     
                  
			 
		          
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