We show that verifying a given prefix code for optimality requires /spl Omega/(nlogn) time, indicating that the verification problem is not asymptotically easier than the construction problem. Alternatively, we give linear-time verification algorithms for several special cases that are either typical in practice or theoretically interesting.

Summary form only given. A new scheme for transmitting sensitive data is proposed, the proposed scheme depends on partitioning the output of a block encryption module using the Chinese Remainder Theorem among a set of channels. The purpose of using the Chinese Remainder Theorem is to hide the cipher text in order to increase the difficulty of attacking the cipher. The proposed scheme assumes the existence of a set of transmission channels between the sender and the receiver parties from which S channels are chosen using some selection criteria. The message is divided into as set of blocks of a size that is a multiple of the size of the underlying block cipher block size. The resulting N bit encrypted block is used as an N-bits integer. This integer remainders with respect to S selected relatively prime numbers are sent over the S selected channels. On the receiver side the inverse Chinese remainder is applied to get the encrypted blocks followed by a decryption operation to construct the original message. The theory, implementation and the security of this scheme are described in the paper.

Summary form only given. Consider the scenario in which a start-up communication company charges its network users by the cost of the minimum spanning tree (MST) they use in their protocols. Wanting to increase their profits, they aim at maximizing the cost of the MST of their network. We consider two different cases. In the first case, the company has a set of links with fixed cost vector W and wants to configure the network so that the MST of the network has the maximum possible cost. In the second case, the network topology is fixed, but the costs on the links assume d different values W/sub 1/, W/sub 2/, ..., W/sub d/ over the day. The company wants to fix the link costs to a value W~ = /spl Sigma//sub i/ p/sub i/ w/sub i/, for some weights p/sub 1/, p/sub 2/, ..., p/sub d/ where 0 /spl les/ p/sub i/ /spl les/ 1 and /spl Sigma//sub i/p/sub i/ = 1, so that the resulting network has a maximum-cost MST.