在分布式环境中生成均匀分布的随机数

Question

I have to generate a "unique Random Number" in a Wireless sensor network which works on the principle of Gossiping.

The requirements are:

1. Each node has to generate a unique Random Number , without having any shared knowledge of what other nodes have generated.
2. The Distribution of the generated Random number should be uniform with respect to each other .
3. It would be preferable if the range of the generated random number is around 10-16 bits or may be lesser.

The limitations are:

1. One node has no idea what number the other nodes in the network are generating.
2. Implementation in C, C++.

I also have the provision of using a unique seed for random number generation. the seed could be any number in the range 0-2^15 .

If there is no way of generating such numbers, then it would be helpful if there is any method by which I can meet some of the above requirements.

If you can suggest me some way to achieve this result it would be really helpful.

Answer 1

for this solution to work you must know the total number of nodes in the generation network. let this number be n .

the basic idea is to generate uniformly distributed random numbers on each participating node inside a given interval. the n intervals of the participating nodes must not overlap. a shared seed does not complicate matters if the total number of nodes does not change and each node can be assigned statically some integer i <= n such that each number is issued exactly once. instead of generating a single random number on each turn, n numbers are generated, and node i takes the i -th number from this series.

however, the overall distribution of random numbers generated will not be uniform unless ...:

• you synchronize random number generation.
• all intervals have the same size.

for information on random number generation on individual nodes see here .