an answer to this Stackoverflow Question http://stackoverflow.com/questions/24683435/iteratively-remove-columns-and-rows-from-a-matrix-s-t-the-mean-value-of-the-row)

mat_minima.R

values <- c(2,5,3,6,7,
            9,5,4,9,9,
            1,5,4,8,1,
            3,1,5,6,2,
            2,9,4,7,4)
my.mat <- matrix(values, nrow = 5, byrow = TRUE)

library(dplyr)
library(tidyr)


colmins <- lapply(1:ncol(my.mat),function(s){col <- my.mat[,s,drop = FALSE]
                                             which(col == min(col), arr.ind = TRUE)}
)

cs_pos <- data.frame(name = rep(paste0("c",1:ncol(my.mat)),
                                times = sapply(colmins,nrow)),
                     do.call(rbind,colmins),
                     stringsAsFactors = FALSE)

rowmins <- lapply(1:nrow(my.mat),function(s){row <- my.mat[s,,drop = FALSE]
                                             which(row == min(row), arr.ind = TRUE)}
)

rs_pos <- data.frame(name = rep(paste0("r",1:nrow(my.mat)),
                                times = sapply(rowmins,nrow)),
                     do.call(rbind,rowmins),
                     stringsAsFactors = FALSE)

cs_val <- data.frame(type = "c", name = paste0("c",1:ncol(my.mat)),
                     val = apply(my.mat,2,min),
                     stringsAsFactors = FALSE)

rs_val <- data.frame(type = "r", name = paste0("r",1:ncol(my.mat)),val = apply(my.mat,1,min),
                     stringsAsFactors = FALSE)


cs <- cs_pos %>%
  mutate(col = col + (extract_numeric(name)-1)) %>%
  left_join(cs_val)

rs <- rs_pos %>%
  mutate(row = row + (extract_numeric(name)-1)) %>%
  left_join(rs_val)


my.df <- rbind(cs,rs)


findpairs <- function(var) xor(duplicated(var,incomparables = NA),
                               duplicated(var,fromLast = TRUE,incomparables = NA))

my.df.dup <- my.df %>%
  mutate(coord = paste(row,col,sep = ",")) %>%
  select(coord,name,type) %>%
  spread(type,name) %>%
  mutate(cdup = findpairs(c),
         rdup = findpairs(r)) %>%
  group_by(coord) %>%
  mutate(nval = sum(!is.na(c),!is.na(r)),
         dup = any(cdup,rdup)) %>%
  mutate(grp = ifelse(nval == 1 & !dup, 1, 0),
         grp = ifelse(nval == 1 & dup, 2, grp),
         grp = ifelse(nval == 2 & !dup, 3, grp),
         grp = ifelse(nval == 2 & dup, 4, grp)) %>%
  arrange(grp) %>%
  select(coord,c,r,grp) 

## nval = 1, dup = FALSE : unique minima
## nval = 1, dup = TRUE  : duplicated minima, unshared
## nval = 2, dup = FALSE : a row-column pair
## nval = 2, dup = TRUE  : >=2 columns share minima with a row (or vice-versa)

my.df.not4 <- my.df.dup %>%
  filter(grp != 4) %>%
  ungroup %>%
  filter(!(grp == 2 & duplicated(c)))

my.df.4 <- my.df.dup %>% 
  ungroup %>%
  filter(grp == 4) %>%
  group_by(c) %>%
  mutate(c_new = ifelse(sample(!duplicated(c)),c,NA)) %>%
  ungroup %>%
  group_by(r) %>%
  mutate(r_new = ifelse(sample(!duplicated(r)),r,NA)) %>%
  ungroup %>%
  select(coord, c = c_new, r = r_new)
  

my.df.names <- rbind(my.df.not4,my.df.4) %>% 
  gather(type,name,c:r,na.rm = TRUE) %>%
  group_by(coord) %>%
  mutate(size = n(),
         name = ifelse(size == 2, paste(name,collapse = ","), name)) %>%
  select(coord,name) %>%
  ungroup

my.df.mins <- my.df %>%
  mutate(coord = paste(row,col,sep = ",")) %>%
  select(coord,val) %>%
  arrange(val %>% desc) %>%
  ungroup


output <- left_join(data.frame(my.df.names),my.df.mins) %>%
  unique %>%
  arrange(desc(val)) %>%
  group_by(val) %>%
  mutate(namesamp = sample(name))

output$namesamp