Partially Persistent Data Structures of Bounded Degree with Constant Update Time

The problem of making bounded in-degree and out-degree data structures partially persistent is considered. The node copying method of Driscoll et al. is extended so that updates can be performed in worst-case constant time on the pointer machine model. Previously it was only known to be possible in amortised constant time.The result is presented in terms of a new strategy for Dietz and Raman's dynamic two player pebble game on graphs.It is shown how to implement the strategy and the upper bound on the required number of pebbles is improved from 2b+2d+O(√b) to d+2b. where b is the bound of the in-degree and d the bound of the out-degree. We also give a lower bound that shows that the number of pebbles depends on the out-degree d.

[1]  Rajeev Raman,et al.  Eliminating Amortization: On Data Structures with Guaranteed Response Time , 1993 .

[2]  Alexander Aiken,et al.  Decidability of Systems of Set Constraints with Negative Constraints , 1994, Inf. Comput..

[3]  Noam Nisan,et al.  Symmetric Logspace is Closed Under Complement , 1994 .

[4]  Rajeev Raman,et al.  Persistence, amortization and randomization , 1991, SODA '91.

[5]  Thore Husfeldt.  Fully Dynamic Transitive Closure in Plane Dags with One Source and One Sink , 1995, ESA.

[6]  Søren Riis.  Count( $q$) versus the pigeon-hole principle , 1997, Arch. Math. Log..

[7]  Robert E. Tarjan,et al.  Making data structures persistent , 1986, STOC '86.

[8]  Søren Riis.  Bootstrapping the Primitive Recursive Functions by 47 Colors , 1994 .

[9]  G. Winskel,et al.  A Compositional Proof System for the Modal mu-Calculus , 1994 .

[10]  Robert E. Tarjan,et al.  Planar point location using persistent search trees , 1986, CACM.

[11]  Ivan Damgård,et al.  Secure Signature Schemes Based on Interactive Protocols See Back Inner Page for a List of Recent Publications in the Brics Report Series. Copies May Be Obtained by Contacting: Secure Signature Schemes Based on Interactive Protocols , 1995 .

[12]  Torben Braüner,et al.  A Model of Intuitionistic Affine Logic from Stable Domain Theory (Revised and Expanded Version) , 1994 .

[13]  Vladimiro Sassone.  Strong Concatenable Processes: An Approach to the Category of Petri Net Computations , 1994 .