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I am trying to understand TTC algorithm for house allocation. I have got a small problem. I am trying to understand the following example:

IE=[i1 , i2 , i3 , i4], IN=[i5], Ho=[h1 , h2 , h3 , h4], and Ho=[h5 , h6 , h7]

The above example is using the Ho variable twice (which is not correct). Somebody please guide me what could be the other variable:

I got the following image:

Example 5p1

The link of the paper is:

House Allocation with Existing Tenant

Somebody please guide me.

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I think this is a typo in the paper. As far as I see, the houses $\{h_5, h_6, h_7\}$ are not occupied, so it should be that $H_V = \{h_5, h_6, h_7\}$.

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