Testing the Necklace Condition for Shortest Tours and Optimal Factors in the Plane

A tour τ of a finite set P of points is a necklace-tour if there are disks with the points in P as centers such that two disks intersect if and only if their centers are adjacent in τ. It has been observed by Sanders that a necklace-tour is an optimal traveling salesman tour.

[1]  Nimrod Megiddo,et al.  Towards a Genuinely Polynomial Algorithm for Linear Programming , 1983, SIAM J. Comput..

[2]  Leonidas J. Guibas,et al.  Optimal Point Location in a Monotone Subdivision , 1986, SIAM J. Comput..

[3]  Kurt Mehlhorn,et al.  Graph Algorithm and NP-Completeness , 1984 .

[4]  J. O'Rourke.  Art gallery theorems and algorithms , 1987 .

[5]  Christos H. Papadimitriou,et al.  The Euclidean Traveling Salesman Problem is NP-Complete , 1977, Theor. Comput. Sci..

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

[7]  W. B. Johnson,et al.  Extensions of Lipschitz mappings into Hilbert space , 1984 .

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

[9]  R. Duffin.  On fourier’s analysis of linear inequality systems , 1974 .

[10]  G. Rothe.  Two solvable cases of the Traveling Salesman Problem , 1988 .

[11]  D. Avis,et al.  REMARKS ON THE SPHERE OF INFLUENCE GRAPH , 1985 .

[12]  G. Toussaint.  Solving geometric problems with the rotating calipers , 1983 .

[13]  A. Barrett.  Network Flows and Monotropic Optimization. , 1984 .

[14]  D. Rose,et al.  Generalized nested dissection , 1977 .

[15]  E. Balas.  Integer and Fractional Matchings , 1981 .

[16]  N. Tomizawa,et al.  On some techniques useful for solution of transportation network problems , 1971, Networks.

[17]  C. Berge.  Graphes et hypergraphes , 1970 .

[18]  Thomas Ottmann,et al.  Algorithms for Reporting and Counting Geometric Intersections , 1979, IEEE Transactions on Computers.

[19]  P. Erdös,et al.  Geometrical Extrema Suggested by a Lemma of Besicovitch , 1951 .

[20]  Robert E. Shostak,et al.  Deciding Linear Inequalities by Computing Loop Residues , 1981, JACM.

[21]  David R. Karger,et al.  Finding the hidden path: time bounds for all-pairs shortest paths , 1991, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science.

[22]  Harold N. Gabow,et al.  An efficient reduction technique for degree-constrained subgraph and bidirected network flow problems , 1983, STOC.

[23]  James R. Munkres,et al.  Topology; a first course , 1974 .

[24]  J. Orlin.  Working Paper Alfred P. Sloan School of Management Genuinely Polynominal Simplex and Non-simplex Algorithms for the Minimum Cost Flow Problem Genuinely Polynominal Simplex and Non-simplex Algorithms for the Minimum Cost Flow Problem , 2008 .

[25]  Maurice Queyranne,et al.  The Time-Dependent Traveling Salesman Problem and Its Application to the Tardiness Problem in One-Machine Scheduling , 1978, Oper. Res..

[26]  D. R. Fulkerson,et al.  Some Properties of Graphs with Multiple Edges , 1965, Canadian Journal of Mathematics.

[27]  Vitit KANTABUTRA,et al.  Traveling Salesman Cycles are not Always Subgraphs of Voronoi Duals , 1983, Inf. Process. Lett..

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

[29]  Richard M. Karp,et al.  Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems , 1972, Combinatorial Optimization.

[30]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[31]  Günter Rote,et al.  Testing the Necklace Condition for Shortest Tours and Optimal Factors in the Plane , 1987, ICALP.

[32]  E. R. Reifenberg.  A Problem on Circles , 1948 .

[33]  D. T. Lee,et al.  On k-Nearest Neighbor Voronoi Diagrams in the Plane , 1982, IEEE Transactions on Computers.

[34]  M. Cutler.  Efficient special case algorithms for the n-line planar traveling salesman problem , 1980, Networks.

[35]  Christos H. Papadimitriou,et al.  On the complexity of integer programming , 1981, JACM.

[36]  Fred Supnick,et al.  A CLASS OF COMBINATORIAL EXTREMA , 1970 .