pred_succ {rPref}

Predecessor and Successor Functions

Description

Functions for traversing the BTG (Better-Than-Graph or Hasse diagram) of a preference.

Usage

init_pred_succ(p, df = NULL)

hasse_pred(p, v, intersect = FALSE)

hasse_succ(p, v, intersect = FALSE)

all_pred(p, v, intersect = FALSE)

all_succ(p, v, intersect = FALSE)

Arguments

p

A preference. Worse tuples in the induced order are successors and better tuples are predecessors.

df

(optional) A data frame characterizing the set wherein predecessors/successors are searched. If df is NULL then the data frame associated with the preference is used. Causes an error if df == NULL and no data frame is associated.

v

A numeric vector of indices in df. This represents the set of tuples for which predecessors/successors are searched.

intersect

(optional) Logical value. If it is FALSE (by default) the union of all predecessors/successors of v is returned. For intersect = TRUE the intersection of those values is returned.

Details

These functions return the predecessors and successors in the Better-Than-Graph of a preference. Note that the successors/predecessors can can be plotted via get_btg. Before any of the successor/predecessor functions can be used the initialization has to be called as follows:

init_pred_succ(p, df)

There p is a preference object and df a data frame. When this done, the data frame df is associated with p, i.e., implicitly assoc.df is called. If the preference has already an associated data frame, df can be omitted. For example

p <- low(mpg, df = mtcars)
init_pred_succ(p)

does the initialization of the preference low(mpg) on the data set mtcars.

The init_pred_succ function calculates the Better-Than-Relation on df w.r.t. p. Afterwards the predecessor and successor functions, as subsequently described, can be called. The value of v is a numeric vector within 1:nrow(df) and characterizes a subset of tuples in df. The return value of these functions is again a numeric vector referring to the row numbers in df and it is always ordered ascending, independently of the order of the indices in v.

all_pred(p, v)

Returns all predecessors of v, i.e., indices of better tuples than v.

all_succ(p, v)

Returns all successors of v, i.e., indices of worse tuples than v.

hasse_pred(p, v)

Returns the direct predecessors of v, i.e., indices of better tuples than v where the better-than-relation is contained in the transitive reduction.

hasse_succ(p, v)

Returns the direct successors of v, i.e., indices of worse tuples than v where the better-than-relation is contained in the transitive reduction.

If v has length 1, then the value of intersect does not matter, as there is nothing to intersect or join. For scalar values x and y the following identities hold, where f is one of the predecessor/successor functions:

f(p, c(x, y), intersect = FALSE) == union(f(p, x), f(p, y))

f(p, c(x, y), intersect = TRUE) == intersect(f(p, x), f(p, y))

Examples

# Preference on mtcars for high mpg and low weight
p <- high(mpg) * low(wt)
init_pred_succ(p, mtcars)

# Helper to show mpg/hp values
show_vals <- function(x) mtcars[x,c('mpg','wt')]

# Pick some tuple "in the middle":
show_vals(10)

# Show (direct) predecessors/successors of tuple 10:
show_vals(hasse_pred(p, 10)) # Next better car
show_vals(hasse_succ(p, 10)) # Next worse car
show_vals(all_pred(p, 10))   # All better cars
show_vals(all_succ(p, 10))   # All worse cars