On routing in circulant graphs

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1627, Issue , 1999, Pages 360-369

  Cai, Jin Yi ^a   Havas, George ^b   Mans, Bernard ^c   Nerurkar, Ajay ^a   Seifert, Jean Pierre ^d   Shparlinski, Igor ^c  

^a State University of New York   (United States)

^b UNIVERSITY OF QUEENSLAND   (Australia)

^c MACQUARIE UNIVERSITY   (Australia)

^d GOETHE UNIVERSITY   (Germany)

Author keywords

Circulant graphs; Diameter; Lattices; Loops; Shortest paths

Indexed keywords

ALGORITHMS; COMBINATORIAL MATHEMATICS; CRYSTAL LATTICES; NUMBER THEORY; POLYNOMIAL APPROXIMATION;

CIRCULANT GRAPHS; DIAMETER; GEOMETRY OF NUMBERS; LOOPS; NP-HARDNESS RESULTS; PSEUDO-POLYNOMIAL TIME ALGORITHMS; SHORTEST PATH; UPPER AND LOWER BOUNDS;

GRAPH THEORY;

EID: 48049110260     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-48686-0_36     Document Type: Conference Paper

References (30)

1. M. Ajtai. Generating hard instances of lattice problems. In Proc. 28th Annual ACM Symposium on the Theory of Computing (1996) 99-108
2. M. Ajtai. The shortest vector problem in L2 is NP-hard for randomized reductions. In Proc. 30th Annual ACM Symposium on the Theory of Computing (1998) 10-19
3. M. Ajtai and C. Dwork. A public-key cryptosystem with worst-case/average-case equivalence. In Proc. 29th ACM Symposium on Theory of Computing (1997) 284- 293
4. S. Arora, L. Babai, J. Stern, and Z. Sweedyk. The hardness of approximate optima in lattices, codes, and systems of linear equations. In Proc. 34th IEEE Symposium on Foundations of Computer Science (FOCS), 724-733, 1993
5. J.-C. Bermond, F. Comellas and D. F. Hsu. Distributed loop computer networks: A survey. Journal of Parallel and Distributed Computing 24 (1995) 2-10
6. J-Y. Cai. A relation of primal-dual lattices and the complexity of shortest lattice vector problem. Theoretical Computer Science 207 (1998) 105-116
7. J-Y. Cai and A. Nerurkar. An improved worst-case to average-case connection for lattice problems. In Proc. 38th IEEE Symposium on Foundations of Computer Science (1997) 468-477
8. e) is NP-hard under randomized reductions. In Proc. 13th Annual IEEE Conference on Computational Complexity (1998) 46-55
9. J. W. S. Cassels. An introduction to the geometry of numbers. Springer-Verlag, 1959
10. N. Chalamaiah and B. Ramamurty. Finding shortest paths in distributed loop networks. Inform. Proc. Letters 67 (1998) 157-161
11. Y. Cheng and F. K. Hwang. Diameters of weighted loop networks. J. of Algorithms 9 (1988) 401-410
12. J. A. Dias da Silva and Y. O. Hamidoune. Cyclic spaces for Grassmann derivatives and additive theory Bull. Lond. Math. Soc. 26 (1994) 140-146
13. I. Dinur, G. Kindler and S. Safra. Approximating-CVP to within almost- polynomial factors is NP-hard. 1998
14. P. Erdös and H. Heilbronn On the addition of residue classes mod p Acta Arithm. 9 (1964) 149-159
15. O. Goldreich and S. Goldwasser. On the limits of non-approximability of lattice problems. In Proc. 30th Annual ACM Symposium on the Theory of Computing (1998) 1-9
16. O. Goldreich, S. Goldwasser and S. Halevi. Collision-free hashing from lattice problems. 1996. Available as TR96-042 from Electronic Colloquium on Computational Complexity at http://www.eccc.uni-trier.de/eccc/.
17. O. Goldreich, S. Goldwasser and S. Halevi. Eliminating decryption errors in the Ajtai-Dwork cryptosystem. Advances in Cryptology - CRYPTO '97 (editor B. Kaliski Jr.), Lecture Notes in Computer Science 1294 (Springer Verlag, 1997) 105-111
18. O. Goldreich, S. Goldwasser and S. Halevi. Public-key cryptosystems from lattice reduction problems. Advances in Cryptology - CRYPTO '97 (editor B. Kaliski Jr.), Lecture Notes in Computer Science 1294 (Springer Verlag, 1997) 112-131
19. D. J. Guan. Finding shortest paths in distributed loop networks. Inform. Proc. Letters 65 (1998) 255-260
20. J. C. Lagarias. The computational complexity of simultaneous diophantine approximation problems. In Proc. 23rd IEEE Symposium on Foundations of Computer Science (1982) 32-39
21. F. T. Leighton. Introduction to parallel algorithms and architectures: Arrays, trees, hypercubes. M. Kaufmann, 1992
22. A. K. Lenstra, H. W. Lenstra and L. Lovász. Factoring polynomials with rational coefficients. Mathematische Annalen 261 (1982) 515-534
23. B. Mans. Optimal Distributed algorithms in unlabeled tori and chordal rings. Journal on Parallel and Distributed Computing 46 (1997) 80-90
24. D. Micciancio. The shortest vector in a lattice is hard to approximate to within some constant. In Proc. 39th IEEE Symposium on Foundations of Computer Science (1998) 92-98
25. A. Paz and C. P. Schnorr. Approximating integer lattices by lattices with cyclic factor groups. Automata, Languages and Programming, 14th International Colloquium, Lecture Notes in Computer Science 267 (Springer-Verlag, 1987) 386-393
26. R. Raz. Personal communication.
27. C. P. Schnorr. A hierarchy of polynomial time basis reduction algorithms. Theoretical Computer Science 53 (1987) 201-224
28. J-P. Seifert and J. Blömer. On the complexity of computing short linearly indepen- dent vectors and short bases in a lattice. To appear in the proceedings of STOC 1999
29. P. van Emde Boas. Another NP-complete partition problem and the complexity of computing short vectors in lattices. Technical Report 81-04, Mathematics Department, University of Amsterdam, 1981
30. J. Žervonik and T. Pisanski. Computing the diameter in multi-loop networks. J. of Algorithms 14 (1993) 226-243.