Introductory discrete mathematics /
V.K. Balakrishnan.
- Dover ed.
- New York : Dover Publications, 1996.
- xiv, 236 p. : ill. ; 24 cm.
- Dover books on mathematics .
"An unabridged, corrected republication of the work first published by Prentice Hall, Englewood Cliffs, N.J., 1991"--T.p. verso.
Includes bibliographical references (p. 219-223) and index.
Set theory and logic. Introduction to set theory ; Functions and relations ; Inductive proofs and recursive definitions -- Combinatorics. Two basic counting rules ; Permutations ; Combinations ; More on permutations and combinations ; The pigeonhole principle ; The inclusion-exclusion principle ; Summary of results in combinatorics -- Generating functions. Ordinary generating functions ; Exponential generating functions -- Recurrence relations. Homogeneous recurrence relations ; Inhomogeneous recurrence relations ; Recurrence relations and generating functions ; Analysis of algorithms -- Graphs and digraphs. Adjacency matrices and incidence matrices ; Joining in graphs ; Reaching in digraphs ; Testing connectedness ; Strong orientation of graphs -- More on graphs and digraphs. Eulerian paths and Eulerian circuits ; Coding and de Bruijn digraphs ; Hamiltonian paths and Hamiltonian cycles ; Applications of Hamiltonian cycles ; Vertex coloring and planarity of graphs -- Trees and their applications. Spanning trees ; Binary trees -- Spanning tree problems. More on spanning trees ; Kruskal's greedy algorithm ; Prim's greedy algorithm ; Comparison of the two algorithms -- Shortest path problems. Dijkstra's algorithm ; Floyd-Warshall algorithm ; Comparison of the two algorithms -- What is NP-completeness? Problems and their instances ; The size of an instance ; Algorithm to solve a problem ; The "Big Oh" or the O(·) notation ; Easy problems and difficult problems ; the Class P and the Class NP ; Polynomial transformations and NP-completeness ; Coping with hard problems.