Suppose there are N parties. Each party has R records, each of which
has D dimensions.

For example, N=3, parties are P1, P2, P3.
D=4, dimensions are named as (A,B,C,D).
R=2, P1 has records T1=(a1,b1,c1,d1),T2=(a2,b1,c2,d1);
P2 has records T3=(a1,b1,c1,d1),T4=(a2,b1,c2,d3);
P3 has records T5=(a1,b1,c1,d1),T6=(a1,b1,c2,d4);

Then, the 3-party union on dimension A ={T1.A, T2.A, ..., T6.A}={4*a1,
2*a2};
union on B={T1.B, T2.B, ..., T6.B}={6*b1};
union on C={3*c1,3*c2};
union on D={4*d1,d3,d4};

The mathematical problem is: given the parties and their records, the
parties want to find whether each record T has the property that the
value on T.A appears at least k1 times in the 3-party union on
dimension A, the value on T.B appears at least k2 times in the union
on B, the value on T.C appears at least k3 times in the union on C,
and the value on T.D appears at least k4 times in the union on D.

For example, when k1=k2=k3=k4=2, T2 has this property, because a2, b1,
c2, d1 appear at least 2 times in the 3-party union on dimension
A, B, C, D respectively. T1, T3, T5 have also the property, but T4 and
T6 haven't.

Is there any application for this problem? I mean, given the parties
and their records, what are the motivations to find such a property? I
find some applications in customer management in chain stores, and
intrusion alert in distributed network monitoring, but
feel that they are still not very appropriate.

Can anybody help me? Thanks a lot!

Simon

Simon,

I am not sure if I understand correctly - you have dimensions from A
to D and have values from 1 to 4 and want to make sure that at least
one entry exists for each combination. - Anyway any SQL product should
be able to do that if you created proper tables. I could think at one
lookup table ("Dimensions") which contains all these combinations and
then two other tables such as "Parties" (one column "PartyCode"
containing P1, P2 etc which is primary key) and
"PartyDimensions" (columns PartyCode, TNumber, Dimension,
DimensionValue). Then you should be able to join the "Dimensions"
table with the "PartyDimensions" and find out what combinations do not
exist - in your example it is D2 which is missing. An other query
could find out the count of each dimension / dimension value
combination. - Look at some SQL books and examples to find out how.

and orders where you want to see which products are not ordered by a
customer and how many were ordered in total for each one.

brgds

Philipp Post

Simon,

I am not sure if I understand correctly - you have dimensions from A
to D and have values from 1 to 4 and want to make sure that at least
one entry exists for each combination. - Anyway any SQL product should
be able to do that if you created proper tables. I could think at one
lookup table ("Dimensions") which contains all these combinations and
then two other tables such as "Parties" (one column "PartyCode"
containing P1, P2 etc which is primary key) and
"PartyDimensions" (columns PartyCode, TNumber, Dimension,
DimensionValue). Then you should be able to join the "Dimensions"
table with the "PartyDimensions" and find out what combinations do not
exist - in your example it is D2 which is missing. An other query
could find out the count of each dimension / dimension value
combination. - Look at some SQL books and examples to find out how.

and orders where you want to see which products are not ordered by a
customer and how many were ordered in total for each one.

brgds

Philipp Post

Simon,

I am not sure if I understand correctly - you have dimensions from A
to D and have values from 1 to 4 and want to make sure that at least
one entry exists for each combination. - Anyway any SQL product should
be able to do that if you created proper tables. I could think at one
lookup table ("Dimensions") which contains all these combinations and
then two other tables such as "Parties" (one column "PartyCode"
containing P1, P2 etc which is primary key) and
"PartyDimensions" (columns PartyCode, TNumber, Dimension,
DimensionValue). Then you should be able to join the "Dimensions"
table with the "PartyDimensions" and find out what combinations do not
exist - in your example it is D2 which is missing. An other query
could find out the count of each dimension / dimension value
combination. - Look at some SQL books and examples to find out how.

and orders where you want to see which products are not ordered by a
customer and how many were ordered in total for each one.

brgds

Philipp Post

This sounds like a version of the golf partnership puzzle. How many
ways can you group (n) people into (t) teams such that no two people
play together more than (x) times?

This sounds like a version of the golf partnership puzzle. How many
ways can you group (n) people into (t) teams such that no two people
play together more than (x) times?

This sounds like a version of the golf partnership puzzle. How many
ways can you group (n) people into (t) teams such that no two people
play together more than (x) times?

On Jun 14, 5:38 am, --CELKO-- <jcelko... (AT) earthlink (DOT) net> wrote:
Hi, dear Philipp and Celko, thank you very much! I've finally found
some motivations for variants of this problem, but not for this
original problem.

One variant is to treat each record as a time series, in which the
dimensions A, B, C, D, etc are successive time points, the values are
categorical values describing a trend property on the corresponding
time. For example, a record can be (Up, Up, Up, Up) which means on the
4 time points there are all upward trend on the measured object. The
measured object can be sales of a commodity or something else.

Then if each vendor holds such a record describing trend on sales of a
commodity, for example, vendor 1 has T1=(Up, Up, Up, Up), vendor 2 has
T2=(Up, Down, Up, Down), vendor 3 has T3=(Down, Up, Down, Up), there
is a motivation for each vendor to check whether on all time points
his trend is as the same as 2/3 (majority) vendors. In this example,
T1 has this property. From this, the vendors can find whether on the
successive time points their sales trend follows the majority of the
vendors.

On Jun 14, 5:38 am, --CELKO-- <jcelko... (AT) earthlink (DOT) net> wrote:
Hi, dear Philipp and Celko, thank you very much! I've finally found
some motivations for variants of this problem, but not for this
original problem.

One variant is to treat each record as a time series, in which the
dimensions A, B, C, D, etc are successive time points, the values are
categorical values describing a trend property on the corresponding
time. For example, a record can be (Up, Up, Up, Up) which means on the
4 time points there are all upward trend on the measured object. The
measured object can be sales of a commodity or something else.

Then if each vendor holds such a record describing trend on sales of a
commodity, for example, vendor 1 has T1=(Up, Up, Up, Up), vendor 2 has
T2=(Up, Down, Up, Down), vendor 3 has T3=(Down, Up, Down, Up), there
is a motivation for each vendor to check whether on all time points
his trend is as the same as 2/3 (majority) vendors. In this example,
T1 has this property. From this, the vendors can find whether on the
successive time points their sales trend follows the majority of the
vendors.

On Jun 14, 5:38 am, --CELKO-- <jcelko... (AT) earthlink (DOT) net> wrote:
Hi, dear Philipp and Celko, thank you very much! I've finally found
some motivations for variants of this problem, but not for this
original problem.

One variant is to treat each record as a time series, in which the
dimensions A, B, C, D, etc are successive time points, the values are
categorical values describing a trend property on the corresponding
time. For example, a record can be (Up, Up, Up, Up) which means on the
4 time points there are all upward trend on the measured object. The
measured object can be sales of a commodity or something else.

Then if each vendor holds such a record describing trend on sales of a
commodity, for example, vendor 1 has T1=(Up, Up, Up, Up), vendor 2 has
T2=(Up, Down, Up, Down), vendor 3 has T3=(Down, Up, Down, Up), there
is a motivation for each vendor to check whether on all time points
his trend is as the same as 2/3 (majority) vendors. In this example,
T1 has this property. From this, the vendors can find whether on the
successive time points their sales trend follows the majority of the
vendors.