It sounds like you're looking for bedtools, which allows you to find the intersection of regions (among other things):

$ cat algo1.bed
chr1    100 1000
chr1    5000    6000
$ cat algo2.bed
chr1    150 1200
chr1    7000    8000
$ intersectBed -a algo1.bed -b algo2.bed
chr1    150 1000

You may also check multiIntersectBed, which is part of the bedtools package and is discussed towards the bottom (second answer from me) of this Biostar thread. I plan to release this on the Galaxy Tool Shed in the next month.

EDIT: More explicit example.

Extend your example two to individuals, A and B.

$ cat all.txt 
A   chr1    100 1000    alg1
A   chr1    150 1200    alg2
A   chr1    5000    6000    alg1
A   chr1    7000    8000    alg2 
B   chr1    100 1000    alg1
B   chr1    150 1200    alg2
B   chr1    5000    6000    alg1
B   chr1    7000    8000    alg2

Use awk to split the file into distinct ind/alg files.

awk '{outfile=$1"_"$5".bed"; print $2"\t"$3"\t"$4 >> outfile}' all.txt

List the resulting files as a sanity check. Note the use of ">>" to create and append to files named (outfile=) based on the ind ($1) and the alg. ($5):

ls -1 *_*.bed
A_alg1.bed
A_alg2.bed
B_alg1.bed
B_alg2.bed

Use multiIntersectBed to find intervals that are common to multiple files. The fourth column is the count of files in which the interval is present. The fifth is a list of the file labels (-names argument) in which the intervals were found. The rest of the columns are T/F indicators of whether the interval was found in each file.

multiIntersectBed -i A_alg1.bed A_alg2.bed B_alg1.bed B_alg2.bed -names A1 A2 B1 B2
chr1    100 150 2   A1,B1   1   0   1   0
chr1    150 1000    4   A1,A2,B1,B2 1   1   1   1
chr1    1000    1200    2   A2,B2   0   1   0   1
chr1    5000    6000    2   A1,B1   1   0   1   0
chr1    7000    8000    2   A2,B2   0   1   0   1

You can then use awk or a simple Perl script to limit the results to those intervals involving two or more algs. for the same individual.

Or, more simply, you could just do a separate command for each individual and just look for output where column 4 is >= 2:

multiIntersectBed -i A_alg1.bed A_alg2.bed -names A1 A2 
chr1    100 150 1   A1  1   0
chr1    150 1000    2   A1,A2   1   1
chr1    1000    1200    1   A2  0   1
chr1    5000    6000    1   A1  1   0
chr1    7000    8000    1   A2  0   1

multiIntersectBed -i A_alg1.bed A_alg2.bed -names A1 A2 | awk '$4>1'
chr1    150 1000    2   A1,A2   1   1

I hope this helps.