I am reading a research paper in which following equation is given: $\underset{\small{X}\\\text{s.t}\sum_{(i,k)\in \mathcal{A}}x_{ik}=1, \forall i\in \mathcal{M}}{\operatorname{max}} u$

where $\small{X}$ is a binary variable that collects all $x_{i,k}$

$\mathcal{M}$ is a set of clients and say its elements are $\mathcal{M} = \{1,2,3,4\}$,

$k$ denotes the node such that $k = \{1,2\}$ i.e., there are two nodes and four clients in the system.

$\mathcal{A}$ is a set of all possible combination of node and client, so there will be 8 elements in it and is given by $\mathcal{A} = \{(1,1),(2,1),(3,1),(4,1),(1,2),(2,2),(3,2),(4,2)\}$.

$u = \sum_{(i,k)\in \mathcal{A}}a_{ik}x_{ik}$ and let say $a_{ik} = 1$ for simplicity.

Also $\mathcal{S}$ is a subset of $\mathcal{A}$ such that $x_{i,k}=1$ if $(i,k)\in \mathcal{S}$ and $x_{i,k}=0$ otherwise, for all $(i,k)\in \mathcal{A}$.

My query is how the such that expression will be equal to one.

Any help in this regard will be highly appreciated.

  • $\begingroup$ "I am reading a research paper". Please cite that paper. It would be great if you can provide a version that is available freely. $\endgroup$
    – John L.
    Aug 4 at 19:59
  • $\begingroup$ Thank u for your reply sir..."Distributed association control and relaying in millimeter wave wireless networks". This is the title of paper and in this equation (3a). For simplicity , I had skipped the summation of this equation that belongs to triplet.... $\endgroup$
    – chaaru
    Aug 5 at 4:27


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