A Birds Eye View to Path Problems

The paper surveys the main results which concern path problems and their complexity. The shortest path problem and its general solution techniques are discussed. Generalized path problems are treated and upper and lower complexity bounds presented. Extensive bibliographic notes are given. The paper is intended to expose the state of a theory which is like a paradigm a means for the study of design and analysis of algorithms.

[1]  Samuel Eilenberg,et al.  Automata, languages, and machines. A , 1974, Pure and applied mathematics.

[2]  Thomas L. Magnanti,et al.  Deterministic network optimization: A bibliography , 1977, Networks.

[3]  Vaughan R. Pratt.  The Power of Negative Thinking in Multiplying Boolean Matrices , 1975, SIAM J. Comput..

[4]  I. N. Sneddon,et al.  Theory Of Automata , 1969 .

[5]  E. Kay,et al.  Graph Theory. An Algorithmic Approach , 1975 .

[6]  R. Backhouse,et al.  Regular Algebra Applied to Path-finding Problems , 1975 .

[7]  Peter A. Bloniarz,et al.  A shortest-path algorithm with expected time O(n2 log n log* n) , 1980, STOC '80.

[8]  Michael L. Fredman,et al.  New Bounds on the Complexity of the Shortest Path Problem , 1976, SIAM J. Comput..

[9]  Donald B. Johnson,et al.  Algorithms for Shortest Paths , 1973 .

[10]  Hartmut Noltemeier,et al.  Graphentheorie : mit Algorithmen und Anwendungen , 1975 .

[11]  Robert A. Wagner,et al.  A Shortest Path Algorithm for Edge-Sparse Graphs , 1976, J. ACM.

[12]  Stuart E. Dreyfus,et al.  An Appraisal of Some Shortest-Path Algorithms , 1969, Oper. Res..

[13]  Michael J. Fischer,et al.  Boolean Matrix Multiplication and Transitive Closure , 1971, SWAT.

[14]  Donald B. Johnson,et al.  Efficient Algorithms for Shortest Paths in Sparse Networks , 1977, J. ACM.

[15]  Daniel J. Lehmann,et al.  Algebraic Structures for Transitive Closure , 1976, Theor. Comput. Sci..

[16]  J. Ian Munro,et al.  Efficient Determination of the Transitive Closure of a Directed Graph , 1971, Inf. Process. Lett..

[17]  I. Anderson,et al.  Graphs and Networks , 1981, The Mathematical Gazette.

[18]  W. Domschke.  Kürzeste Wege in Graphen: Algorithmen, Verfahrensvergleiche , 1972 .

[19]  R. Tarjan.  Solving path problems on directed graphs. , 1975 .

[20]  Ahnont Wongseelashote.  Semirings and path spaces , 1979, Discret. Math..

[21]  A. Pierce.  Bibliography on Algorithms for Shortest Path, Shortest Spanning Tree, and Related Circuit Routing Problems (1956-1974) , 1975, Networks.

[22]  B. Carré.  An Algebra for Network Routing Problems , 1971 .