Mathematics for Computer Science

9.10. Scheduling 253 underwear shirt jacket left shoe right shoe belt left sock right sock pants tie A 1 A 2 A 3 A 4 Figure 9.9 ...

Chapter 9 Directed graphs & Partial Orders254 two different elements in the set are comparable. A chain is said toend atan i ...

9.10. Scheduling 255 Theorem 9.10.6.Letbe a strict partial order on a set,A. A minimum length schedule forconsists of the sets ...

Chapter 9 Directed graphs & Partial Orders256 Corollary 9.10.11.Every partially ordered set withnelements has a chain of siz ...

9.12. Summary of Relational Properties 257 For example, suppose thatADZandx R ymeans thatxy .mod5/. Then Œ7çRDf:::;3;2;7;12;22; ...

Chapter 9 Directed graphs & Partial Orders258 ReflexivityRisreflexivewhen 8 x 2 A: x R x: Every vertex inRhas a self-loop. I ...

9.12. Summary of Relational Properties 259 Path-Total Rispath-totalwhen 8 x¤y 2 A: .x R y ORy R x/ Given any two vertices inR, t ...

Chapter 9 Directed graphs & Partial Orders260 1 2 4 3 5 6 Figure 9.10 DAG with edges not needed in paths The following examp ...

9.12. Summary of Relational Properties 261 (c)Prove that every finite tournament digraph has a ranking. (d)Prove that the less-t ...

Chapter 9 Directed graphs & Partial Orders262 a b d c king king king not a king Figure 9.11 A 4-chicken tournament in which ...

9.12. Summary of Relational Properties 263 letRndenote the length-nwalk relation in the digraphR, that is, a RnbWWDthere is a le ...

Chapter 9 Directed graphs & Partial Orders264 A digraph isweakly connectedif there is a “path” between any two vertices that ...

9.12. Summary of Relational Properties 265 +0 +1 +0 +0 +1 +1 +1 00 11 10 01 +0 Figure 9.12 The 2-bit graph. minimum length for a ...

Chapter 9 Directed graphs & Partial Orders266 Problems for Section 9.7 Class Problems Problem 9.12. Direct Prerequisites Sub ...

9.12. Summary of Relational Properties 267 (c)What are the maximal and minimal elements? Are they maximum and mini- mum? (d)Answ ...

Chapter 9 Directed graphs & Partial Orders268 (e)The empty relation on the set of real numbers. (f)The identity relation on ...

9.12. Summary of Relational Properties 269 Homework Problems Problem 9.21. LetRandSbe transitive binary relations on the same se ...

Chapter 9 Directed graphs & Partial Orders270 under product, ifR 1 R 2 has the property whenever bothR 1 andR 2 have the pr ...

9.12. Summary of Relational Properties 271 that is a DAG with these subjects as vertices. 18:01!6:042 18:01!18:02 18:01!18:03 6: ...

Chapter 9 Directed graphs & Partial Orders272 5.Open a Starbucks chainfor the army to get their caffeine - 10 days, after ta ...