Q:

Find the intersection of overlapping ranges in two tables using data.table function foverlaps

I would like to use foverlaps to find the intersecting ranges of two bed files, and collapse any rows containing overlapping ranges into a single row. In the example below I have two tables with genomic ranges. The tables are called "bed" files that have zero-based start coordinates and one-based ending positions of features in chromosomes. For example, START=9, STOP=20 is interpreted to span bases 10 through 20, inclusive. These bed files can contain millions of rows. The solution would need to give the same result, regardless of the order in which the two files to be intersected are provided.
First Table
> table1
   CHROMOSOME START STOP
1:          1     1   10
2:          1    20   50
3:          1    70  130
4:          X     1   20
5:          Y     5  200

Second Table
> table2
   CHROMOSOME START STOP
1:          1     5   12
2:          1    15   55
3:          1    60   65
4:          1   100  110
5:          1   130  131
6:          X    60   80
7:          Y     1   15
8:          Y    10   50

I was thinking that the new foverlaps function could be a very fast way to find the intersecting ranges in these two table to produce a table that would look like:
Result Table:
> resultTable
   CHROMOSOME START STOP
1:          1     5   10
2:          1    20   50
3:          1   100  110
4:          Y     5   50  

Is that possible, or is there a better way to do that in data.table?
I'd also like to first confirm that in one table, for any given CHROMOSOME, the STOP coordinate does not overlap with the start coordinate of the next row. For example, CHROMOSOME Y:1-15 and CHROMOSOME Y:10-50 would need to be collapsed to CHROMOSOME Y:1-50 (see Second Table Rows 7 and 8). This should not be the case, but the function should probably check for that. A real life example of how potential overlaps should be collapsed is below:
   CHROM  START   STOP
1:     1 721281 721619
2:     1 721430 721906
3:     1 721751 722042

Desired output:
   CHROM  START   STOP
1:     1 721281 722042

Functions to create example tables are as follows:
table1 <- data.table(
   CHROMOSOME = as.character(c("1","1","1","X","Y")) ,
   START = c(1,20,70,1,5) ,
   STOP = c(10,50,130,20,200)
)

table2 <- data.table(
   CHROMOSOME = as.character(c("1","1","1","1","1","X","Y","Y")) ,
   START = c(5,15,60,100,130,60,1,10) ,
   STOP = c(12,55,65,110,131,80,15,50)
 )

A:

@Seth provided the fastest way to solve the problem of intersection overlaps using the data.table foverlaps function. However, this solution did not take into account the fact that the input bed files may have overlapping ranges that needed to be reduced into single regions. @Martin Morgan solved that with his solution using the GenomicRanges package, that did both the intersecting and range reducing. However, Martin's solution didn't use the foverlaps function. @Arun pointed out that the overlapping ranges in different rows within a table was not currently possible using foverlaps. Thanks to the answers provided, and some additional research on stackoverflow, I came up with this hybrid solution.
Create example BED files without overlapping regions within each file.
chr <- c(1:22,"X","Y","MT")

#bedA contains 5 million rows
bedA <- data.table(
    CHROM = as.vector(sapply(chr, function(x) rep(x,200000))),
    START = rep(as.integer(seq(1,200000000,1000)),25),
    STOP = rep(as.integer(seq(500,200000000,1000)),25),
    key = c("CHROM","START","STOP")
    )

#bedB contains 500 thousand rows
bedB <- data.table(
  CHROM = as.vector(sapply(chr, function(x) rep(x,20000))),
  START = rep(as.integer(seq(200,200000000,10000)),25),
  STOP = rep(as.integer(seq(600,200000000,10000)),25),
  key = c("CHROM","START","STOP")
)

Now create a new bed file containing the intersecting regions in bedA and bedB.
#This solution uses foverlaps
system.time(tmpA <- intersectBedFiles.foverlaps(bedA,bedB))

user  system elapsed 
1.25    0.02    1.37 

#This solution uses GenomicRanges
system.time(tmpB <- intersectBedFiles.GR(bedA,bedB))

user  system elapsed 
12.95    0.06   13.04 

identical(tmpA,tmpB)
[1] TRUE

Now, modify bedA and bedB such that they contain overlapping regions:
#Create overlapping ranges
makeOverlaps <-  as.integer(c(0,0,600,0,0,0,600,0,0,0))
bedC <- bedA[, STOP := STOP + makeOverlaps, by=CHROM]
bedD <- bedB[, STOP := STOP + makeOverlaps, by=CHROM]

Test time to intersect bed files with overlapping ranges using either the foverlaps or GenomicRanges fucntions.
#This solution uses foverlaps to find the intersection and then run GenomicRanges on the result
system.time(tmpC <- intersectBedFiles.foverlaps(bedC,bedD))

user  system elapsed 
1.83    0.05    1.89 

#This solution uses GenomicRanges
system.time(tmpD <- intersectBedFiles.GR(bedC,bedD))

user  system elapsed 
12.95    0.04   12.99 

identical(tmpC,tmpD)
[1] TRUE

The winner: foverlaps!
FUNCTIONS USED
This is the function based upon foverlaps, and will only call the GenomicRanges function (reduceBed.GenomicRanges) if there are overlapping ranges (which are checked for using the rowShift function).
intersectBedFiles.foverlaps <- function(bed1,bed2) {
  require(data.table)
  bedKey <- c("CHROM","START","STOP")
  if(nrow(bed1)>nrow(bed2)) {
    bed <- foverlaps(bed1, bed2, nomatch = 0)
  } else {
    bed <- foverlaps(bed2, bed1, nomatch = 0)
  }
  bed[, START := pmax(START, i.START)]
  bed[, STOP := pmin(STOP, i.STOP)]
  bed[, `:=`(i.START = NULL, i.STOP = NULL)]
  if(!identical(key(bed),bedKey)) setkeyv(bed,bedKey)
  if(any(bed[, STOP+1 >= rowShift(START), by=CHROM][,V1], na.rm = T)) {
    bed <- reduceBed.GenomicRanges(bed)
  }
  return(bed)
}

rowShift <- function(x, shiftLen = 1L) {
  #Note this function was described in this thread:
  #http://stackoverflow.com/questions/14689424/use-a-value-from-the-previous-row-in-an-r-data-table-calculation
  r <- (1L + shiftLen):(length(x) + shiftLen)
  r[r<1] <- NA
  return(x[r])
}

reduceBed.GenomicRanges <- function(bed) {
  setnames(bed,colnames(bed),bedKey)
  if(!identical(key(bed),bedKey)) setkeyv(bed,bedKey)
  grBed <- makeGRangesFromDataFrame(bed,
    seqnames.field = "CHROM",start.field="START",end.field="STOP")
  grBed <- reduce(grBed)
  grBed <- data.table(
    CHROM=as.character(seqnames(grBed)),
    START=start(grBed),
    STOP=end(grBed),
    key = c("CHROM","START","STOP"))
  return(grBed)
}

This function strictly used the GenomicRanges package, produces the same result, but is about 10 fold slower that the foverlaps funciton.
intersectBedFiles.GR <- function(bed1,bed2) {
  require(data.table)
  require(GenomicRanges)
  bed1 <- makeGRangesFromDataFrame(bed1,
    seqnames.field = "CHROM",start.field="START",end.field="STOP")
  bed2 <- makeGRangesFromDataFrame(bed2,
    seqnames.field = "CHROM",start.field="START",end.field="STOP")
  grMerge <- suppressWarnings(intersect(bed1,bed2))
  resultTable <- data.table(
    CHROM=as.character(seqnames(grMerge)),
    START=start(grMerge),
    STOP=end(grMerge),
    key = c("CHROM","START","STOP"))
  return(resultTable)
}

An additional comparison using IRanges
I found a solution to collapse overlapping regions using IRanges but it is more than 10 fold slower than GenomicRanges.    
reduceBed.IRanges <- function(bed) {
  bed.tmp <- bed
  bed.tmp[,group := { 
      ir <-  IRanges(START, STOP);
      subjectHits(findOverlaps(ir, reduce(ir)))
    }, by=CHROM]
  bed.tmp <- bed.tmp[, list(CHROM=unique(CHROM), 
              START=min(START), 
              STOP=max(STOP)),
       by=list(group,CHROM)]
  setkeyv(bed.tmp,bedKey)
  bed[,group := NULL]
  return(bed.tmp[, -(1:2)])
}

system.time(bedC.reduced <- reduceBed.GenomicRanges(bedC))

user  system elapsed 
10.86    0.01   10.89 

system.time(bedD.reduced <- reduceBed.IRanges(bedC))

user  system elapsed 
137.12    0.14  137.58 

identical(bedC.reduced,bedD.reduced)
[1] TRUE

A:

foverlaps() will do nicely.
First set the keys for both of the tables:
setkey(table1, CHROMOSOME, START, STOP)
setkey(table2, CHROMOSOME, START, STOP)

Now join them using foverlaps() with nomatch = 0 to drop unmatched rows in table2.
resultTable <- foverlaps(table1, table2, nomatch = 0)

Next choose the appropriate values for START and STOP, and drop the extra columns.
resultTable[, START := pmax(START, i.START)]
resultTable[, STOP := pmin(STOP, i.STOP)]
resultTable[, `:=`(i.START = NULL, i.STOP = NULL)]

The overlapping STOP to a future START should be a different question. It's actually one that I have, so maybe I'll ask it and come back to it here when I have a good answer.

