I usually try to use levels to fix my data before hand:
x <- structure(list(V1 = c("a", "y", "w", "p", "v", "h", "i"),
V2 = c("r", "w", "q", "m", "l", "q", "g"), V3 = c(
"5", "2", "9", "2", "1", "3", "0")), .Names = c("V1", "V2",
"V3"), class = "data.frame", row.names = c(NA, -8L))
x <- x[1:7,]
x$V1 <- factor(x$V1, levels=(x$V1)[order(x$V3)])
# Note it's not an ordered factor, it's a factor in the right order
ggplot(x, aes(V1, V3)) + geom_tile()
UPDATE:
Still not exactly clear on your dimensions, but perhaps something like:
x$V2 <- factor(x$V2, levels=(x$V2)[order(x$V3)])
ggplot(x, aes(V1,V2,fill=V3)) + geom_tile()
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