# How to read and interpret these expressions?

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.

• "I am reading a research paper". Please cite that paper. It would be great if you can provide a version that is available freely. Aug 4 at 19:59
• 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.... Aug 5 at 4:27