Re: Faster ways to unionize intersecting sets?

• To: mathgroup at smc.vnet.net
• Subject: [mg70183] Re: Faster ways to unionize intersecting sets?
• From: "lsha" <lsha at earthlink.net>
• Date: Sat, 7 Oct 2006 07:06:50 -0400 (EDT)
• References: <eg02a3\$81m\$1@smc.vnet.net> <eg2e4o\$70u\$1@smc.vnet.net>

Hi,

I tried mergeSets2[] and the answer is different from mergeSets[].
An example:
In[34]:=
s = {{1, 2}, {2, 3}, {4, 5}, {6, 7}, {7, 5}, {9, 10}, {11, 12}, {13, 14}};

In[35]:=
mergeSets[s]
Out[35]=
{{1, 2, 3}, {4, 5, 6, 7}, {9, 10}, {11, 12}, {13, 14}}

In[36]:=
mergeSets2[s]
Out[36]=
{{{9, 10}, {11, 12}, {13, 14}}, {1, 2, 3, 4, 5, 6, 7}}

The non-intersecting singles are correct but the intersecting sets are all
merged together with mergeSets2[].

Regards,
Ling Sha

"Jean-Marc Gulliet" <jeanmarc.gulliet at gmail.com> wrote in message
news:eg2e4o\$70u\$1 at smc.vnet.net...
> lsha wrote:
>> Hi,
>>
>> I need to search a list of sets and unionize any sets that intersect. The
>> following functions seems to work but may be there are faster ways?
>>
>>
>>
>>
>> intersectQ[s1_, s2_] := If[Intersection[s1, s2] != {}, True, False]
>>
>> mergeSets[s_List] := Module[
>> {h, r, singles, club, cnt},
>> cnt = Length[s];
>> If[cnt < 2, Return[s]];
>> singles = {};
>> club = s;
>>
>> While[cnt >= 2,
>> h = club[[1]];
>> r = Rest[club];
>> hit = 0;
>> club = If[intersectQ[h, #], hit = 1; Union[h, #], #] & /@ r;
>> If[hit == 0, singles = Append[singles, h]];
>> --cnt;
>> ];
>> Join[singles, club]
>> ]
>>
>>
> Using functional programming, mergeSets2 (see In[5]) is 15 to 20 times
> faster than the original procedural code.
>
> In[1]:=
> intersectQ[s1_, s2_] := If[Intersection[s1, s2] != {},
>    True, False]
> mergeSets[s_List] := Module[{h, r, singles, club,
>     cnt}, cnt = Length[s]; If[cnt < 2, Return[s]];
>     singles = {}; club = s; While[cnt >= 2,
>      h = club[[1]]; r = Rest[club]; hit = 0;
>       club = (If[intersectQ[h, #1], hit = 1;
>            Union[h, #1], #1] & ) /@ r;
>       If[hit == 0, singles = Append[singles, h]];
>       --cnt; ]; Join[singles, club]]
>
> In[3]:=
> s = Table[Table[Random[Integer, {1, 1000}],
>      {Random[Integer, {1, 20}]}], {100}];
>
> In[4]:=
> t1 = Timing[res1 = mergeSets[s]; ][[1]]
>
> Out[4]=
> 1.234 Second
>
> In[5]:=
> mergeSets2[s_List] := Module[{list, pos, singles,
>     club}, list = MapIndexed[Intersection[#1,
>         Flatten[Drop[s, #2]]] & , s];
>     pos = Position[list, {}]; singles =
>      Extract[s, pos]; club =
>      Union[Flatten[Complement[s, singles]]];
>     {singles, club}]
>
> In[6]:=
> t2 = Timing[res2 = mergeSets2[s]; ][[1]]
>
> Out[6]=
> 0.063 Second
>
> In[7]:=
> t1/t2
>
> Out[7]=
> 19.5873
>
> Regards,
> Jean-Marc
>

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