Align ggplot2 plots vertically

With the code found at https://gist.github.com/low-decarie/5886616 A dual dendodogram tile plot can be produced:

dual_dendogram_tile_plot(as.matrix(USArrests), main="USA Arrests")

The problem: Align the vertical dendogram with the tile plot area. (and/or improve the alignment of the horizontal dendogram)

This question relates to:

left align two graph edges (ggplot)
Specifying ggplot2 panel width Plot correlation matrix into a graph

Here's an example to align more basic grobs,

library(ggplot2)
library(grid)
library(gtable)

p <- qplot(1,1)
g <- ggplotGrob(p)

panel_id <- g$layout[g$layout$name == "panel",c("t","l")]
g <- gtable_add_cols(g, unit(1,"cm"))

g <- gtable_add_grob(g, rectGrob(gp=gpar(fill="red")),
                     t = panel_id$t, l = ncol(g))

g <- gtable_add_rows(g, unit(1,"in"), 0)
g <- gtable_add_grob(g, rectGrob(gp=gpar(fill="blue")),
                     t = 1, l = panel_id$l)

grid.newpage()
grid.draw(g)

and with your grobs

The answer from @baptiste helped me get a better understanding of the gtable structure and how to modify it. Below I post just my modified variant as code snippet for (my own) reuse.

It is using find_panel() to get the panel extent, and pipes %>% the modifications directly into grid.draw. The piping considerably simplified playing around with the gtable_* functions, as it allows to easily uncomment single lines and check the effect on the final plot.

library(ggplot2)
library(grid)
library(gtable)
library(dplyr)

p <- ggplot(tribble(~x,~y,~a,~b, 
                    1, 1, "a1","b1",
                    1, 1, "a2","b1",
                    1, 1, "a2","b2"), 
           aes(x=x,y=y)) + 
  geom_point() + 
  facet_grid(vars(a),vars(b))

g <- ggplotGrob(p)
panels_extent <- g %>% find_panel()
g %>%
  # Add red box to the very right, by appending a column and then filling it
  gtable_add_cols(widths = unit(1,"cm"), pos = -1) %>%
  gtable_add_grob(rectGrob(gp=gpar(fill="red")),
                  t = panels_extent$t, b = panels_extent$b,
                  l = -1, r = -1) %>%
  # Add green box to the top, by prepending a row and then filling it
  # Note the green box extends horizontally over the first panel as well 
  # as the space in between.
  gtable_add_rows(heights = unit(1,"cm"), pos = 0) %>%
  gtable_add_grob(rectGrob(gp=gpar(fill="green")),
                  t = 1, b = 1,
                  l = panels_extent$l, r = panels_extent$l+1) %>%
  {grid.newpage();grid.draw(.)}