Get Matrices in Combinatorics and Graph Theory (Network Theory PDF

By Bolian Liu

ISBN-10: 0792364694

ISBN-13: 9780792364696

The 1st bankruptcy of this booklet offers a short therapy of the fundamentals of the topic. the opposite chapters take care of many of the decompositions of non-negative matrices, Birkhoff style theorems, the research of the powers of non-negative matrices, purposes of matrix how to different combinatorial difficulties, and purposes of combinatorial the right way to matrix difficulties and linear algebra difficulties. The insurance of must haves has been saved to a minimal. however, the ebook is largely self-contained (an Appendix presents the mandatory historical past in linear algebra, graph conception and combinatorics). there are lots of routines, all of that are observed via sketched ideas. viewers: The booklet is acceptable for a graduate direction in addition to being a very good reference and a helpful source for mathematicians operating within the zone of combinatorial matrix conception.

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Monma and S. Suri, Transitions in geometric minimum spanning trees. Discrete Comput. Geom. 8 (1992), 265-293. M. Mount, The number of shortest paths on the surface of a polyhedron, SIAM J. Comput. 19 (1990), 593-611. [112] R. MuUin and R. Stanton, A map-theoretic approach to Davenport-Schinzel sequences. Pacific J. Math. 40 (1972), 167-172. [113] K. Mulmuley, Hidden surface removal with respect to a moving point, Proc. 23rd Annu. ACM Sympos. Theory Comput. (1991), 512-522. [114] K. Mulmuley, On levels in arrangements and Voronoi diagrams.

A shortest path on the surface of a convex poly tope can be represented by the sequence of edges that it crosses, and we refer to such a sequence of edges as a shortestpath edge sequence. It is known that there are 6)(n'*) shortest path edge-sequences [111, 133]. Agarwal et al. [4] have shown that the exact set of all shortest-path edge sequences can be computed in time 0{n^Xs (n) \ogn), for some constant ^ > 0, improving a previous algorithm by Schevon and O'Rourke [134]. Baltsan and Sharir [28] considered the special case where O consists of two disjoint convex poly topes (and p and q lie anywhere in the free space).

34] J. H. Reif, New lower bound techniques for robot motion planning problems, Proc. 28th Annu. IEEE Sympos. Found. Comput. Sci. (1987), 49-60. [35] B. Chazelle, H. Edelsbrunner, L. Guibas, M. Sharir and J. Snoeyink, Computing a face in an arrangement of line segments and related problems, SIAM J. Comput. 22 (1993), 1286-1302. [36] B. J. Guibas, Fractional cascading: I. A data structuring technique, Algorithmica 1 (1986), 133-162. [37] B. T. Lee, On a circle placement problem. Computing 36 (1986), 1-16.

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Matrices in Combinatorics and Graph Theory (Network Theory and Applications Volume 3) by Bolian Liu


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