I'm working on digital SSR of perennial plant whole chromatin DNA. I found the Interval type very useful in titrating out a chromosome segment containing a reasonable density of alleles of interest. The code ran remarkably fast and had no surprises. One thing I wished for was a built-in IntervalLength function, but perhaps this exists by another name in Geometry or elsewhere.

In the following example, a very long read chromosome assembly is downloaded from GenBank. This is followed by two tunable parameters "allelePositionsSpan" and "maxInitialSeqLen", and then by the alleles of interest.

fStart = AbsoluteTime[];
genbankData = ResourceFunction["ImportFASTA"]["CM019739.1"];
sequenceDescription = genbankData[[1, 1]];
forwardSequence = genbankData[[2, 1]];
fFinish = AbsoluteTime[];
Print[sequenceDescription];
Print["StringLength[forwardSequence] = ", 
  StringLength[forwardSequence]];
Print["elapsed download time = ", SetPrecision[(fFinish - fStart), 3],
   " seconds"];

allelePositionsSpan = 16;
maxInitialSeqLen = 580;
Print["allelePositionsSpan = ", allelePositionsSpan];
Print["maxInitialSeqLen = ", maxInitialSeqLen];

allelesOfInterest = {"GTTT", "TAAT", "TGTT", "TTAA", "TTTA"};
allelesOfInterestCount = Length[allelesOfInterest];
Print["allelesOfInterest = ", allelesOfInterest];

iSstart = AbsoluteTime[];
initialSelections = Table[
   Table[
      If[#[[p + allelePositionsSpan, 2]] - #[[p, 1]] > 
        maxInitialSeqLen,
       Nothing,
       Interval[{#[[p, 1]], #[[p + allelePositionsSpan, 2]]}]],
      {p, 1, Length[#] - allelePositionsSpan}
      ] &[SortBy[StringPosition[forwardSequence, allele], First]],
   {allele, allelesOfInterest}
   ];
iSfinish = AbsoluteTime[];
Print["initialSelections dimensions = ", {allelesOfInterestCount, 
   Length[#] & /@ initialSelections}];
Print["initialSelections elapsed time = ", 
  SetPrecision[(iSfinish - iSstart), 3], " seconds"];

aHstart = AbsoluteTime[];
alleleHashSets = 
  Table[CreateDataStructure["HashSet"], {allele, allelesOfInterest}];
Do[
  imax = Length[initialSelections[[h]]];
  i = 1;
  While[(i < imax),
   mergedInterval = initialSelections[[h, i]];
   notFound = True;
   While[notFound \[And] (i < imax),
    i++;
    intersection = 
     IntervalIntersection[mergedInterval, initialSelections[[h, i]]];
    If[Length[intersection] > 0,
     mergedInterval = 
      IntervalUnion[mergedInterval, initialSelections[[h, i]]],
     (* else *)
     notFound = False;
     ];
    {} (* end While body *)
    ];
   alleleHashSets[[h]]["Insert", mergedInterval];
   {} (* end While body *)
   ];
  {},
  {h, 1, allelesOfInterestCount}
  ];
Clear[initialSelections];
aHfinish = AbsoluteTime[];
Print["alleleHashSets dimensions = ", {allelesOfInterestCount, 
   Length[Normal[#]] & /@ alleleHashSets}];
Print["alleleHashSets elapsed time = ", 
  SetPrecision[(aHfinish - aHstart), 3], " seconds"];

vIstart = AbsoluteTime[];
vettedIntervals = Normal[alleleHashSets[[1]]]; (* initializer *)
Do[
  vettedIntervalsHash = CreateDataStructure["HashSet"];
  Do[
   Do[
    If[Length[IntervalIntersection[vI, aI]] > 0,
     vettedIntervalsHash["Insert", IntervalUnion[vI, aI]]
     ],
    {vI, vettedIntervals}
    ],
   {aI, Normal[alleleHashSets[[a]]]}
   ];
  vettedIntervals = Normal[vettedIntervalsHash];
  Clear[vettedIntervalsHash];
  {},
  {a, 2, allelesOfInterestCount }
  ];
Clear[alleleHashSets];
vIfinish = AbsoluteTime[];
vettedIntervalsLength = Length[vettedIntervals];
Print["vettedIntervalsLength = ", vettedIntervalsLength];
Print["vettedIntervals elapsed time = ", 
  SetPrecision[(vIfinish - vIstart), 3], " seconds"];
If[vettedIntervalsLength > 0,
  iMax = Min[vettedIntervalsLength, 5];
  Print["vettedIntervals (", vettedIntervalsLength, "):"];
  Do[
   Print[i, " : ", vettedIntervals[[i]], ", length ", 
    vettedIntervals[[i, 1, 2]] - vettedIntervals[[i, 1, 1]]];
   Print["\t", 
    "allele counts = ", (Length[
        StringPosition[
         StringTake[forwardSequence, vettedIntervals[[i, 1]]], #]] & /@
       allelesOfInterest)],
   {i, 1, iMax}
   ];
  If[vettedIntervalsLength > iMax, Print["..."]];
  ];

Output:

allelePositionsSpan = 16

maxInitialSeqLen = 580

allelesOfInterest = {GTTT,TAAT,TGTT,TTAA,TTTA}

initialSelections dimensions = {5,{1159,4162,1186,6408,14353}}

initialSelections elapsed time = 3.52 seconds

alleleHashSets dimensions = {5,{177,648,168,975,1787}}

alleleHashSets elapsed time = 0.107 seconds

vettedIntervalsLength = 1

vettedIntervals elapsed time = 0.109 seconds

vettedIntervals (1):

1 : Interval[{13255103,13257036}], length 1933

allele counts = {32,27,30,25,47}