Mathematics for Computer Science

10.9. Bene ̆s Network 293 in 0 in 1 in 2 out 0 out 1 out 2 (b)Give an input/output permutation, 0 , that forces maximum congest ...

Chapter 10 Communication Networks294 through the same subnetwork because a collision would occur in the next-to-last column of s ...

10.9. Bene ̆s Network 295 in 0 in 1 in 2 in 3 out 0 out 1 out 2 out 3 the first layer to the corresponding switch in the second ...

Chapter 10 Communication Networks296 in 0 in 2 in 4 out 0 out 1 out 2 out 3 out 4 in 1 in 3 Figure 10.5 5-Path new, better commu ...

10.9. Bene ̆s Network 297 Homework Problems Problem 10.7. Louis Reasoner figures that, wonderful as the Beneˇs network may be, t ...

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11 Simple Graphs Simple graphsmodel relationships that aresymmetric, meaning that the relationship is mutual. Examples of such m ...

Chapter 11 Simple Graphs300 simple graph only has an undirected edge,hv—wi, that connectsvandw. Definition 11.1.1.Asimple graph, ...

11.2. Sexual Demographics in America 301 that the degree of every vertex is also zero. But a simple graph must have at least one ...

Chapter 11 Simple Graphs302 M F Figure 11.2 The sex partners graph vertices equals the number of edges. So these sums are equal: ...

11.3. Some Common Graphs 303 but there are fewer males, so they have a higher ratio. This means that the Uni- versity of Chicago ...

Chapter 11 Simple Graphs304 Figure 11.3 K 5 : the complete graph on 5 nodes. Figure 11.4 An empty graph with 5 nodes. Ann-node g ...

11.4. Isomorphism 305 Figure 11.6 C 5 : a 5-node cycle graph. b c a d (a) 2 3 1 4 (b) Figure 11.7 Two Isomorphic graphs. 11.4 Is ...

Chapter 11 Simple Graphs306 Figure 11.8 IsomorphicC 5 graphs. Here is an isomorphism,f, between the two graphs in Figure 11.7: f ...

11.5. Bipartite Graphs & Matchings 307 isomorphic that isguaranteedto run in polynomial time on all pairs of graphs.^3 Havin ...

Chapter 11 Simple Graphs308 Chuck Tom Michael John Alice Martha Sara Jane Mergatroid Figure 11.9 A graph where an edge between a ...

11.5. Bipartite Graphs & Matchings 309 Chuck Tom Michael John Alice Martha Sara Jane Mergatroid Figure 11.10 One possible ma ...

Chapter 11 Simple Graphs310 Inductive Step: We need to show that 8 km:P.k/IMPLIESP.mC1/. Suppose thatjMjDmC 1  2. Case 1: Ever ...

11.5. Bipartite Graphs & Matchings 311 neighborsof some setSof vertices is the image ofSunder the edge-relation, that is, N. ...

Chapter 11 Simple Graphs312 It follows thatdjN.S/j djSj. Cancellingdcompletes the derivation of equa- tion (11.2).  Regular gr ...