Implements an algorithm for the
house allocation problem proposed by Abdulkadiroglu and Sonmez (1999) for a matching problem in which there are both vacant houses and existing tenants.

ttc(nStudents = ncol(s.prefs), nHouses = length(houses), s.prefs,
houses, priority = NULL, seed = 123)

## Arguments

nStudents |
integer indicating the number of students. Defaults to `ncol(s.prefs)` . |

nHouses |
integer indicating the number of houses. Defaults to `length(houses)` . |

s.prefs |
matrix of dimension `nHouses` x `nStudents` with column j containing student jth ranking over houses in decreasing order of preferences (i.e. most preferred first). |

houses |
vector of length `nHouses` which represents the occupation of the houses. Entry in `k` contains `j` if student `j` is living in house `k` and `NA` if house `k` is vacant. |

priority |
(Optional) vector of length `nStudents` . Gives the prioirity ordering of the students, if nothing is specified a random ordering is chosen. |

seed |
(Optional) integer setting the state for random number generation. Defaults to seed =123. |

## Value

`ttc`

returns a data frame of the matching of students (int) to houses (obj) for the house allocation problem based on the Top-Trading-Cycles algorithm.

## References

Abdulkadiroglu, A. and T. Sonmez (1999). House Allocation with Existing Tenants. *Journal of Economic Theory*, 88 (2): 233-260.

Shapley, L. and H. Scarf (1974). On Cores and Indivisibility. *Journal of Mathematical Economics*, 1(1): 23-37.

## Examples

# NOT RUN {
## 1-a. Generate matrix of individuals' preference rankings over objects,
## a.k.a. Rank Order Lists (ROL).
s.prefs <- matrix(c(3,2,4,1, # ROL of student 1
3,5,6, NA,
3,1, NA,NA,
2,5,6,4,
1,3,2,NA,
2,4,5,6), nrow = 4, ncol = 6, byrow = FALSE); s.prefs
## 1-b. Generate vector of house occupation objects ('obj') and their owners ('ind')
(houses <- 1:6)
## 1-c. Find assignment based on TTC algorithm
ttc(s.prefs = s.prefs, houses = houses, nHouses = 6, priority = 1:6)
## 2-a.Compare the example in the paper Abdulkadiroglu et al. (1999)
## on page 246-248 (section 5.1 An Example):
## generate matrix of students' preference rankings over houses, a.k.a. Rank Order Lists (ROL)
s.prefs <- matrix(c(2,6,5,1,4,3,7,NA,
7,1,6,5,4,3,2,NA,
2,1,4,7,3,6,5,NA,
2,4,3,6,1,7,5,NA,
4,3,7,1,2,5,6,NA), byrow = FALSE, ncol= 5); s.prefs
## 2-b. Generate house occupation, so student 1 lives in house 1, ..., student 4 lives in house 4
## and the other houses are vacant.
houses <- c(1,2,3,4,NA,NA,NA,NA); houses
## 2-c. Generate priority ordering
priority <- 1:5
## 2-d. Find assigment
ttc(s.prefs = s.prefs, houses = houses, priority = priority)
# }