## Mini-Project discussion with Davide

Met with Davide at the whiteboard on the 3rd floor lobby to discuss and mini-project for me to do.

In the context of mobile sensor nodes, he would like to discover if we can reduce the overall total of Neighbors nodes (i.e. the sum over all nodes, of the number of neigbors each node has)

E = SUM(0 to n: total neigbors)

Construct a lattice of size L2 with N nodes, Each node may only move along the lines of the lattice, each costing 1.

Time is discreet, at intervals 1,2,3 … n etc. and

at each time step,

a node at random is picked,

if the node has less than or equal to C neighbors, then it picks one of the four surrounding points, and if that point is empty, it moves to that point, else it stays where it is.

else if the node has a value greater than C neighbours, it will pick a a diagonal position (2 hops) at random, and if it is not occupied, it will move, else it will stay where it is.

(Nodes will not bounce off the side of the lattice, but will continue to the other side.)

We will measure the value of E over T (time), and also the cost of movements.

T is not the timesteps, but each discreet value of T is the next step when each node has on average had the chance to move once (i.e. T is when t equals the number of nodes)

The overall effect should be to reduce density, speedily, as when there are too many neighbors, movement is ‘faster’ i.e. more hops.

The idea is to simulate this to generate some nice graphs