A total of five distinct indices are considered.
We use these two distinct indices because some measurements are not be transmitted.
The properties of A make easy to achieve agreement: at most to distinct indexes are decided since A solves graph convergence.
To explain what these maps are, suppose thati,j and k are the cells' distinct indices and,for convenience, temporarily let s 1 = h, s 2 = m 2, s 3 = m 3 denote the slow variables for the three cells.
Since A solves graph convergence on G, the values it returns y1,y2 and y3 to p1,p2, and p3, respectively, cover a vertex or an edge of G, hence at most two distinct indexes are decided.
For any permutation π of P distinct indices m p ∈{1,…,N} such as q p =π(m p ), p∈{1,…,P}, with P≤N, we have X × q = q 1 q P A ( q ) = X × m = m 1 m P A ( m ) which means that the order of the mode‐ m p products is irrelevant when the indices m p are all distinct.
For the sake of simplicity, we focus on the inputless version of the (n−1 -set agreemen−1 -setem eagreementss problem as input its indeach, and every correct process is required to decide an index of a process that participates in thasexecution such thas at most n−1 dinputct itsexes are decindexby the processes.
Algorithm 5 solves two-set agreement for three robots, p1,p2, and p3, using algorithms A and B. The idea of the solution is that robots use A to "agree" on a vertex or an edge of G, namely, on at most two distinct vertices, and then use these information to return at most two distinct indexes of participating processes.
