For the k-median problems, we define an (a, 6)--approximation algorithm as a

polynomial-time algorithm that computes a solution using at most bk number of facilities with cost at most a times the cost of an optimal solution using at most k facilities.

In general form, scheduling algorithms have been found to be NP-complete (i.e., it is believed that there is no optimal

polynomial-time algorithm for them [4, 5]).

(i) KeyGen([1.sup.[kappa]]), the key pair generation algorithm, is a probabilistic

polynomial-time algorithm which outputs a private/public key pair (sk, pk) on input of domain parameters pp which is an output of the setup algorithm taking a security parameter [kappa] as an input;

To incorporate more practically important factors into scheduling, this work proposes a

polynomial-time algorithm for solving two SMSPs, which takes into account both learning effects and variable maintenance activity.

* XP: For every fixed value of the parameter k, there exists a

polynomial-time algorithm solving the problem on inputs of size n, but the exponent of the running time grows with k, i.e.

--Anonymity against Database: A probabilistic polynomial-time joint computation (P, V, M) has anonymity against database if for any i, j [member of] [n], any [z.sub.1], [z.sub.2] [member of] [{0,1}.sup.m] , any ([w.sub.t]).sub.t[member of][n]] [member of] ([{0,1}.sup.m])n , any probabilistic

polynomial-time algorithm B, and any sufficiently large k,

Then the Quadratic Residue Assumption [3] states that there is no probabilistic

polynomial-time algorithm for computing square roots with respect to modulus N.

There is a new appendix on the recently discovered unconditional deterministic

polynomial-time algorithm for primality testing.

There exists a

polynomial-time algorithm for the prefetch/caching problem on D parallel disks, that produces a solution with at most D times the optimum stall time using at most D - 1 extra memory locations.

Hochbaum and Maass [1985] gave a

polynomial-time algorithm to compute a cover of size (1 + [Epsilon])k*, for any [Epsilon] [is greater than] 0 [1985]; see also Bronnimann and Goodrich [1995], Feder and Greene [1988], and Gonzalez [1991].

The long standing open question, "whether there can be any

polynomial-time algorithm for LP" was resolved when Khachian developed the ellipsoid algorithm.

A problem may remain NP-hard even if restricted to instances with a particular value of the parameter, or there may be a

polynomial-time algorithm for each such value.