Graph and network algorithms

Graphs provide a powerful tool to model objects and relationships among objects. The study of graphs dates back to Euler’s days in the 18th century, when he defined the Konigsberg bridge problem, and since then has been pursued by many researchers. Specifically, graphs can be used to model problems in many areas such as transportation, scheduling, networks, robotics, VLSI, compilers, mathematical biology, and software engineering. Many optimization problems from these and other diverse areas can be phrased in graph-theoretic terms, leading to algorithmic questions about graphs.

[1]  Kenneth Steiglitz,et al.  Combinatorial Optimization: Algorithms and Complexity , 1981 .

[2]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[3]  Robert E. Tarjan,et al.  Depth-First Search and Linear Graph Algorithms , 1972, SIAM J. Comput..

[4]  H. Kuhn.  The Hungarian method for the assignment problem , 1955 .

[5]  Peter Elias,et al.  A note on the maximum flow through a network , 1956, IRE Trans. Inf. Theory.

[6]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[7]  Ioannis G. Tollis,et al.  Algorithms for Drawing Graphs: an Annotated Bibliography , 1988, Comput. Geom..

[8]  J. Hopcroft,et al.  Algorithm 447: efficient algorithms for graph manipulation , 1973, CACM.

[9]  Richard M. Karp,et al.  A n^5/2 Algorithm for Maximum Matchings in Bipartite Graphs , 1971, SWAT.

[10]  J. A. Bondy,et al.  Graph Theory with Applications , 1978 .

[11]  Richard Bellman,et al.  ON A ROUTING PROBLEM , 1958 .

[12]  Robert E. Tarjan,et al.  Data structures and network algorithms , 1983, CBMS-NSF regional conference series in applied mathematics.

[13]  Robert E. Tarjan,et al.  Efficient algorithms for finding minimum spanning trees in undirected and directed graphs , 1986, Comb..

[14]  Robert E. Tarjan,et al.  Fibonacci heaps and their uses in improved network optimization algorithms , 1987, JACM.

[15]  Elwood S. Buffa,et al.  Graph Theory with Applications , 1977 .

[16]  S. N. Maheshwari,et al.  An O(|V|³) Algorithm for Finding Maximum Flows in Networks , 1978, Inf. Process. Lett..

[17]  R. Prim.  Shortest connection networks and some generalizations , 1957 .

[18]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .