Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Given a sum of $l$ integers $r_1+...+r_k+...+r_l$ and an integer $t$.

Find indices

$1 < p_1 <...< p_h <...< p_{t-1} < l$

such that in sum

$(r_1+...+r_{p_1})+...+(r_{p_{h-1}+1}+...+r_{p_h})+...+(r_{p_{t-1}}+...+r_l)$

sums in brackets have nearly same value.

The criteria "nearly same value" can be defined by some norm over the vector of sums $(R_1,...,R_h,...,R_t)$, where $R_h=(r_{p_{h-1}+1}+...+r_{p_h})$.

Do you know something about this problem? Any similar problems? Any suitable references on such problems? To what problems this can be reduced?

share|improve this question
    
Is $t$ specified, or are you allowed to select $t$ as part of the optimization? –  Brian Borchers Apr 21 '11 at 20:37
    
$t$ is specified –  arepo Apr 22 '11 at 0:53
    
One different way of thinking this problem is the following. You have a full bipartite graph. The nodes on the left side represent your $l$ $r_l$ numbers and the vertices on your right represent your $t$ sets. The weights of the edge $e_{i,j}$ is the value $r_i$. Your objective now is to find something like a cardinality and weight "balanced" set cover comprising of $t$ sets. I'm not sure though if this can give you any further insights.. –  Anadim Apr 22 '11 at 2:01

1 Answer 1

For a great result for $t=2$, see this paper by Gyula Karolyi.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.