Computing roadmaps of semi-algebraic sets

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn Part F129452, Issue , 1996, Pages 168-173

  Basu, S ^a   Pollack, R ^a   Roy, M F ^b  

^a NEW YORK UNIVERSITY   (United States)

^b UNIVERSITÉ DE RENNES 1   (France)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; ALGEBRA; BOOLEAN FUNCTIONS; BOUNDARY VALUE PROBLEMS; COMPUTATIONAL COMPLEXITY; GRAPH THEORY; POLYNOMIALS; PROBLEM SOLVING; SET THEORY;

CONNECTED COMPONENT; ROAD-MAPS; SEMI-ALGEBRAIC SET; SEMI-ALGEBRAIC SETS; TWO-POINT;

ALGEBRA; ALGORITHMS;

COMPUTING ROADMAPS; FINITE SUBSET; SEMI ALGEBRAIC SET;

EID: 0029701331     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/237814.237857     Document Type: Conference Paper

References (12)

1. S. BASU, R. POLLACK, M.-F. ROY On the combinatorial and algebraic complexity of Quantifier Elimination, Proc. 35th IEEE Symp. on Foundations of Computer Science, 632-642, (1994), (Journal version to appear in JACM).
2. J. BOCHNAK, M. COSTE, M.-F. ROY Géométrie algébrique réelle. Springer-Verlag (1987).
3. J. CANNY, The Complexity of Robot Motion Planning, MIT Press (1987).
4. J. CANNY, Computing road maps in general semialgebraic sets, The Computer Journal, 36:504-514, (1993).
5. G. E. COLLINS, Quantifier elimination for real closed fields by cylindrical algebraic decomposition. Springer Lecture Notes in Computer Science 33, 515-532.
6. D. GRIGOR'EV, N. VOROBJOV Counting connected components of a semi-algebraic set in subexponential time. Comput. Complexity, 2:133-186 (1992).
7. L. GOURNAY, J. J. RLSLER Construction of roadmaps of semi-algebraic sets. Technical Report, DMI, Ecole Normale Superieure, Paris, France (1992).
8. R. M. HARDT Semi-algebraic Local Triviality in Semialgebraic Mappings. American Journal of Math. 102, 1980, 291-302.
9. J. HEINTZ, M.-F. ROY, P. SOLERNÒ Single exponential path finding in semi-algebraic sets II: The general case. Algebraic geometry and its applications. C. L. Bajaj editor, Springer Verlag (1993) 467-481.
10. J. MLLNOR Morse Theory, Annals of Mathematical Studies, Princeton University Press.
11. J. RENEGAR On the computational complexity and geometry of the first order theory of the reals, J. of Symbolic Computation, (1992).
12. J. SCHWARTZ, M. SHARIR On the 'piano movers' problem II. General techniques for computing topological properties of real algebraic manifolds. Advances in Applied Mathematics 4, 298-351.