k 1 in the worst case, and ( k 1) / 2 in the average case The O-notation was apparently The o-notation was apparently

Transcription

1 Errata for Algorthms Sequetal & Parallel, A Ufed Approach (Secod Edto) Russ Mller ad Laurece Boxer Charles Rver Meda, 005 Chapter 1 P. 3, l. 14- to 13- the worst case, ad / the average case 1 the worst case, ad ( 1) / the average case P. 30, l. 5: The O-otato was apparetly The o-otato was apparetly P. 33, top of page: I the algorthm for MmumIdex, there are three occurreces of at that are t, ut, talczed. Chapter P. 36, l. 9-10: The lst tems umered 1), ), rather tha a), ). P. 38, l. : There a perod at the ed of the le. P. 51, paragraphs aove Suprogram Splt: Therefore, the rug tme of ths smple merge algorthm s Θ (), where s the legth of the frst put lst to e exhausted. Therefore, the rug tme of ths smple merge algorthm s Θ (), where s the umer of odes (from oth put lsts) that have ee merged whe the frst put lst s exhausted. P. 56, l. 6-: I the fucto header, the argumet talczed.

2 Chapter 3 P. 61, l. 3: Let ) ( f, e Let ) ( f e P. 64, l (colo for perod): depeds o the secod summato. Θ = > N f a g / 1, log 0 ) (. depeds o the secod summato: Θ = > N f a g / 1, log 0 ) (.

3 Chapter 4 P. 84, d paragraph: exactly exactly log stages of mergg log stages of mergg

4 Chapter 5 P. 99, ER PRAM Algorthm for Broadcastg: If + 1 the P wrtes d to P 1 If + the P wrtes d to d P. 100, RAM Mmum Algorthm: talcze x If + x < m_so_far P. 101, Fgure 5.4: At Tme Step 3, we should have T 1] = 4, ot 15. P. 105, the algorthm: Output: succeeds, a flag dcatg whether or ot the search succeeds ad locato Output: succeeds, a flag dcatg whether or ot the search succeeds, ad locato P. 17 (talcs): 1/ ( 1/ 1) = 3 1/ 1/ ( 1/ 1) = 3 1/ P. 136, d ad 3 rd les after capto: (log +1) dmesoal (log +1) -dmesoal P. 140, Cost/Wor paragraph: Let T par () represet Let T par () represet

5 Chapter 6 No errata reported. Chapter 7 P. 174, l. 3 up: sucue_prefx talczed. Chapter 8 No errata reported.

6 Chapter 9 P. 08: Item 7 s Else If structure s more easly uderstood usg the followg algmet. Else If smalllst + equallst the retur AM Else {fd result glst} CreateArray(gLst, glst_array) Selecto smalllst equallst, glst _ array,1, glst retur ( ) Ed Else {fd result glst} P. 09, ullet tem dscussg Step 4: We ca smplfy otato y sayg that ths step requres less tha T ( / 5) tme. We ca smplfy otato y sayg that ths step requres T ( / 5) tme. P. 10, tem c), d setece: Thus, the recursve call to Selecto (, smalllst _ array,1, Selecto(, smalllst _ array,1 requres at most T ( 7 /10) tme. Thus, the recursve call to Selecto (, smalllst _ array,1, smalllst ) requres at most T ( 7 /10) tme. P. 10, l. up p. 11, l. 3: Delete the two seteces A upper oud o the rght sde we have T ( ) = O( ).

7 Chapter 10 P. 65, mddle paragraph: It s easy to see how such a approach yelds a ( ) algorthm for the tersecto query prolem, It s easy to see how such a approach yelds a ( ) Θ tme RAM O tme RAM algorthm for the tersecto query prolem, P. 69, Item 5: ( a,,, ) ( a,,, m) o m = ( a,,, m) ( a,,, ) m f a a otherwse. < ad a, ]; m Thus, A o B represets a, ] a, ], provded these arcs tersect, m, m, a, ], ad a ] exteds a ] to the rght more tha does a, Thus, ] ;. Because the tervals are ordered y ther rght edpots,. ( a,,, ) ( a,,, m) o m ( a,,, m) m f a a < m ; = otherwse. ( a,,, ) A o B represets a, ] a, ], provded these arcs tersect m ad a, ] exteds a, ] to the rght more tha does a, ] ;. m Because the tervals are ordered y ther left edpots,. P. 75: The last paragraph should ot e laeled as tem d), as t s a part of tem c).

8 Chapter 11 P. 9, Fgure 11.7: There a arrow from the words colum / to the horzotal ceter of the fgure: row 1 outer order elemet row / row /+1 row er order elemet colum / colum /+1 P. 9, paragraph followg Fgure: There s a ad le rea the equato S (, ) = m S (, ), S (, + 1) + S ( 1, ) { } + 1 +

9 Chapter 1 P. 304, last paragraph: A path such that ( v A path such that ( v, v +1) E., v ) E. +1 P. 33, tem 1: Etry A (, ) tme Etry A (, ) tme P. 34, capto of Fg. 1.: At tme t = 1, At tme t + 1, P. 36: I order to provde the le refereces that are used Fgure 1.5, the algorthm for the star fucto preseted wth les umered as follows: 1. Determe the Boolea fucto star ( v ) for all v V, as follows.. For all vertces v, do parallel 3. star( v) true 4. If root( v) root( root( v )), the 5. star( v) false 6. star( root( v) ) false 7. star( root( root( v) )) false 8. Ed If star v star 10. Ed For 9. ( ) ( root( )) v P. 36 (setece followg star algorthm): See Fgure 1-5 for a example that shows the ecessty of the step mared {*}. See Fgure 1.5 for a example that shows the ecessty of Step 9. P. 33, last setece of frst paragraph: Therefore, the rug tme s O ( E log E), whch s O ( E logv ). Therefore, the rug tme s Θ ( E log E), whch s Θ ( E logv ).

10 P. 33, d paragraph, d setece: Suppose that stead of tally sortg to decreasg order Suppose that stead of tally sortg to odecreasg order P. 346, prolem 6, 3 rd setece: comparg the compoet wth comparg the compoet laels of P. 349, Exercse 9: A partte graph wth susets V,V 0 1 A partte graph wth oempty susets V,V 0 1

11 Chapter 13 P. 353, 6 les from ottom (space): Is Prme true IsPrme true P. 361, Tale 13.1: The colum headers are trasposed. The left colum should have the colum header d. The rght colum should have the colum header d.