Ph.D. Dissertation

Referred Journal Articles

  1. Shen, Z., Static analysis of a mesh system, Information Processing Letters 47(1993) 295-299.
  2. Shen, Z., Drexel, P., and Urbach, L., A mathematical model of a mesh system and its implementation, Mathematical and Computer Modeling 18(2)(1993) 33-48.
  3. Shen, Z., A mathematical model for mesh's dynamic behavior, Computers & Mathematics with Applications 28(6) (1994) 25--32.
  4. Shen, Z., and Marston, C., A study of a dice problem, Applied Mathematics and Computation 73(2-3) (1995) 231-247.
  5. Wasserman, H. C., Yukawa, K., and Shen, Z., The essential inadequacy of deduction in logic programming, The bulletin of IGPL 3(1) (1995) 107-110.
  6. Shen, Z., The average diameter of general tree structures, Computers & Mathematics with Applications 36(7) (1998) 111--130.
  7. Shen, Z., Average diameter and its estimation in the non-linear structures. Computers & Mathematics with Applications 40(2000) 261-276.
  8. Shen, Z., The calculation of average distance in the mesh structures. Computers & Mathematics with Applications 44(2002) 1379-1402.
  9. Shen, Z., A minimal broadcasting schema for the mesh structures. International Journal of High Performance Computing and Networking, 2(3/4/5) (2004) 210-221.
  10. Shen, Z., A study of a generalization of a card problem. Applied Mathematics and Computation 166(2) (2005) 385-410.
  11. Shen, Z., Alleviation of the impact of the apex nodes in the pyramid structures. Applied Mathematics and Computation 169(1) (2005) 157-178.
  12. Shen, Z., A bypassing path based routing algorithm for the pyramid structures. Applied Mathematics and Computation 181 (2006) 1523-1543
  13. Shen, Z., A generalized broadcasting schema for the mesh structures. Applied Mathematics and Computation 186(2) (2007) 1293-1310.
  14. Qiu, K. and Shen, Z., On a combinatorial problem on the star graphs. Congressus Nemerantium 185 (2007) 97-109.
  15. Shen, Z., and Qiu, K., On the Whitney numbers of the second kind for the star poset. European Journal of Combinatorics, 29(7) (2008) 1585-1586.
  16. Shen, Z., and Qiu, K., An explicit formula of the surface area for the star graph and a Proof of its correctness. Congressus Numerantium, 192 (December 2008) 115-127.
  17. Cheng, E., Qiu, K., and Shen, Z., A short note on the surface area of star graphs. Parallel Processing Letters, 19(1) (2009) 19-22.
  18. Shen, Z., Qiu, K., and Cheng, E., On the surface area of the (n, k)-star graph. Theoretical Computer Science 410(52) (2009), 5481-5490.
  19. Cheng, E., Qiu, K., and Shen, Z., A generating function approach to the surface area of some interconnection networks. Journal of Interconnection Networks, 10(3) (2009) 189-204.
  20. Cheng, E., Grossman, J., Liptak, L., Qiu, K., and Shen, Z., Distance formula and shortest paths for the (n,k)-star graphs. Information Sciences 180 (2010) 1671-1680.
  21. Cheng, E., Qiu, K., and Shen, Z., On deriving explicit formulas of the surface areas for the arrangement graphs and some of the related graphs. International Journal of Computer Mathematics 87(13) (2010) 2903-2914
  22. Cheng, E., Qiu, K., and Shen, Z., A note on the surface areas of the product graphs. Congressus Numerantium 203 (2010) 131-137.
  23. Cheng, E., Qiu, K., and Shen, Z., On the surface areas and average distances of meshes and tori. Parallel Processing Letters 21(1) (2011) 61-75.
  24. Cheng, E., Qiu, K., and Shen, Z., A note on the alternating group network. The Journal of Supercomputing 59(1) (2012) 246-248.
  25. Cheng, E., Qiu, K., and Shen, Z., On the surface area of the augmented cubes. Journal of Supercomputing (2011) DOI: 10.1007/s11227-011-0641-1

Referred Conference Papers

  1. Drexel, P., Rucinski, A., and Shen, Z., A probabilistic model of a mesh system with distributed routing, in Proc. of the Pacific-Rim International Conference on Modeling, Simulation and Identification, Vancouver, BC, Canada, 1992, pp. 39-42.
  2. Shen, Z., Drexel, P., and Urbach, L., Packet delay predication in datagram mesh system, in Proc. of the 1993 ACM Symposium on Applied Computing, ACM Press, 1993, pp. 539-545.
  3. Drexel P., Shen, Z., and Urbach L., Characterization and implementation of a mathematical model for a mesh system, in Proc. of the 1993 SCS Simulation Multi-Conference, Arlington, VA, 1993, pp. 176-181.
  4. Wasserman, H. C., Yukawa, K., and Shen, Z., The essential inadequacy of deduction in logic programming (Extended Abstract): in Proc. of the 1993 International Symposium on Logic Programming, MIT Press, 1993, pp. 644.
  5. Wasserman, H. C., and Shen, Z., The locality principle and completeness in logic programming, in Proc. of 1994 ACM Symposium on Applied Computing, ACM Press, 1994, pp. 286-- 291.
  6. Wasserman, H. C., Yukawa, K., and Shen, Z., An alternative transformation rule for logic programming (Extended Abstract), in Proc. of 1995 ACM Symposium on Applied Computing, ACM Press, New York, 1995, pp.364--368.
  7. Wasserman, H. C., Yukawa, K., and Shen, Z., On quantitative measurement of negation in logic programming (Intended Abstract), in Proc. of the 1996 ACM Symposium on Applied Computing, ACM Press, New York, 1996. pp.58-62.
  8. Shen, Z., The average diameter of binary trees structures (Extended Abstract), in Proc. of the 1997 ACM Symposium on Applied Computing, ACM Press, New York, 1997, pp. 40--44.
  9. Shen, Z., Average diameter of network structures and its estimation, in Proc. of the 1998 ACM Symposium on Applied Computing, ACM Press, New York, 1998, pp. 593--597.
  10. Shen, Z., Average diameter and its estimation in the non-linear structures (Intended Abstract), in Proc. of the 1999 ACM Symposium on Applied Computing, ACM Press, New York, 1999, pp. 489--490.
  11. Shen, Z., Calculation of average distance in the mesh structures (Extended Abstract), in Proc. of the 2000 ACM Symp. on Applied Computing. ACM Press, New York, 2000, pp. 89-93.
  12. Shen, Z., A routing algorithm for pyramid structures (Extended Abstract), in Proc. of the 2001 ACM Symp. on Applied Computing, ACM Press, New York, 2001, pp. 484--488.
  13. Shen, Z., An optimal broadcasting schema for the mesh structures, in Proc. of ISCA 17th International Conference on Computing and their Applications, San Francisco, CA, April 2002, pp. 273-276.
  14. Shen, Z., An alternative routing algorithm for the pyramid structures, in Proc. of ISCA 17th International Conference on Computing and their Applications, San Francisco, April 2002, pp. 487-490.
  15. Shen, Z., An optimal broadcasting schema for multidimensional mesh structures (Extended Abstract), in Proc. of the 2003 ACM Symp. on Applied Computing. ACM Press, New York, 2003, pp. 1019--1023.
  16. Shen, Z., An alternative routing algorithm for the pyramid structures (Extended Abstract), in Proc. of the 2003 ACM Symp. on Applied Computing. ACM Press, New York, 2003, pp. 1009--1013.
  17. Shen, Z. and Healy, T., A study of a card problem and its generalization(Extended Abstract), in Proc. of the ISCA 19th International Conference on Computers and Their Applications, Seattle, WA, March 2004, pp. 55-58.
  18. Shen, Z., Alleviation of the impact of the apex nodes in the pyramid structures(Extended Abstract), in Proc. of the ISCA 19th International Conference on Computers and Their Applications, Seattle, WA, March 2004, pp. 168-171.
  19. Berry, J. W., Hrozencik, D., Rao, S., and Shen, Z., Finding Central Sets of Tree Structures in Synchronous Distributed Systems, in Pro. of the 17th International Conference on Parallel and Distributed Computing Systems (PDCS-2004), San Francisco. CA, Sept. 15-17, 2004, pp. 201-208.
  20. Luttamaguzi, J., Pelsmajer, M., Shen, Z, and Yang, B., Integer Programming Methods for Several Optimization Problems in Graph Theory, in the Proc. of, the ISCA 20th International Conference on Computers and Their Applications(CATA-2005), New Orleans, LO, March 16-18, 2005, pp. 50-55.
  21. Berry, J., Hrozencik, D., Rao, S., and Shen, Z., Finding the Median Set of Tree Structures in Synchronous Distributed Systems, in the Proc. of the ISCA 20th International Conference on Computers and Their Applications(CATA-2005), New Orleans, LO, March 16-18, 2005, pp. 7-12.
  22. Shen, Z., A generalized broadcasting schema for the mesh structures(Extended abstract), in the Proc. of ISCA 21st International Conference on Computers and Their Applications(CATA2006), Seattle, WA, March 22-25, 2006, pp. 270-275.
  23. Shen, Z., On the number of spanning trees in a mesh structure, in the Proc. of the 19th International Conf. on Parallel and Distr. Computing System(PDCS-2006), San Francisco, California, Sept. 20-22, 2006, pp. 1-6.
  24. Shen, Z. and Qiu, K., On the effective paths for the general tori, in Proc. of the ISCA 20th International Con. on Parallel and Distributed Computing System(PDCS2007), Las Vegas, NV, Sept. 24-26, 2007, pp. 230-235.
  25. Shen, Z. and Qiu, K., On the vertex disjoint paths for the general tori. in Proc. of the ISCA 20th International Con. on Parallel and Distributed Computing System(PDCS2007), Las Vegas, NV, Sept. 24-26, 2007, pp. 236-241.
  26. He, L., Qiu, K., and Shen, Z., Neighbourhood Broadcasting and Broadcasting on the (n, k)-Star Graph, Proc. of the 8th International Conference on Algorithms and Architectures for Parallel Processing (ICA3PP'08), Cyprus, June 9-11, 2008, Springer LNCS 5022, pp. 70-78.
  27. Shen, Z., Qiu, K., and Cheng, E., On the Surface Area of the (n, k) Star Graph, Proc. of the 2nd Annual International Conference on Combinatorial Optimization and Applications (COCOA'08), August 21-24, 2008, St. Johns, Newfoundland, Canada, Springer LNCS 5165, pp. 393-404.
  28. Cheng, E., Gao, S., Qiu, K., and Shen, Z., An efficient routing algorithm for disjoint shortest paths on Hypercube(Extended Abstract), Proc. the 3rd Annual International Conference on Combinatorial Optimization and Applications (COCOA'09)., June 10-12, 2009, Yellow Mountains, China, Springer LNCS 5573, pp. 375-383.
  29. Cheng, E., Qiu, K., and Shen, Z., On the surface area of the alternating group networks, Proc. IASTED Parallel and Distributed Computing and Systems (PDCS2009), November 2-4, 2009, Cambridge, MA, pp. 85-90.
  30. Cheng, E., Qiu, K., and Shen, Z., The number of shortest paths in the (n,k)-star graphs(Extended Abstract), in Proc. Fourth Annual International Conference on Combinatorial Optimization and Applications (COCOA'2010), Dec. 18-20, 2010, Kailua-Kona, HI, USA, Springer LNCS 6508(Part I), pp.222-236.
  31. Cheng, E., Qiu, K., and Shen, Z., On the surface areas of the asymmetric twisted cubes, in Proc. Fifth Annual International Conference on Combinatorial Optimization and Applications (COCOA'2011), August 4-6, 2011, Zhang Jia Jie, China, Springer LNCS 6831, pp.411-423.

Non-referred Papers

  1. Shen, Z., Correcting an Error in a "Cheat Sheet", SIGACT News 28.1(1997) 49-51.
  2. Berry, J., Hrozencik, D., Rao, S., and Shen, Z., Finding Central Sets of Tree Structures in Synchronous Distributed Systems, Technical Report (2004-07), DIMACS, Rutgers University, 2004.
  3. Luttamaguzi, J., Pelsmajer, M., Shen, Z, and Yang, B., Integer Programming Methods for Several Optimization Problems in Graph Theory. Technical Report (2005-02), DIMACS, Rutgers University, 2005.

Accepted Paper(s)

  1. Cheng, E., Qiu, K., and Shen, Z., On the surface area of the alternating group graphs and the split star graphs. To appear in Ars Combinatoria. Preprint 2008

Submitted Paper(s)

  1. Cheng, E., Liptak, L., Qiu, K., and Shen, Z., Cyclic vertex connectivity of Cayley graphs generated by transposition trees. Submitted to Graphs and Combinatorics. Preprint 2010
  2. Cheng, E., Qiu, K., and Shen, Z., The number of shortest paths in the (n,k)-star graphs. Submitted to Discrete Mathematics, Algorithms and Applications Preprint 2011
  3. Cheng, E., Qiu, K., and Shen, Z., On disjoint shortest paths routing in interconnection networks: a case study in the star graph. Submitted to 24th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA 2012). Preprint 2012
  4. Cheng, E., Qiu, K., and Shen, Z., A generating function approach to the edge surface area of the arrangement graphs. Submitted to The Computer Journal. Preprint 2012
  5. Cheng, E., Grosman, J., Qiu, K., and Shen, Z., A Faster Algorithm for Finding Disjoint Ordering of Sets. Submitted to The 10th IEEE International Symposium on Parallel and Distributed Processing with Applications (ISPA 2012). Preprint 2012
  6. Cheng, E., Qiu, K., and Shen, Z., Edge Centered Surface Areas for the Star Graphs. Submitted to Forty-Third Southeastern International Conference on Combinatorics, Graph Theory, and Computing (CGTC43) Preprint 2012

Paper(s) in preparation

  1. Cheng, E., Qiu, K., and Shen, Z., Length Two Path Centered Surface Area for the Star Graphs.
  2. Cheng, E., Qiu, K., and Shen, Z., The surface area of the arrangement graph centered at an edge.
  3. Cheng, E., Grosman, J., Qiu, K., and Shen, Z., The number of shortest paths in the arrangement graphs.
  4. Cheng, E., Grosman, J., Qiu, K., and Shen, Z., Length Two Path Centered Surface Area for the arrangement Graphs.
  5. Cheng, E., Qiu, K., and Shen, Z., Edge Centered Surface Areas for the (n, k)-Star Graphs.
  6. Cheng, E., Qiu, K., and Shen, Z.,An Estimate of the Conditional Diagnosablilty for Some of the Interconnection Structures