Given a m-by-n matrix with $n>>m$ and with a known rank of $k\leq m$, what would be a computationally effective way of finding out $k$ columns, such that the matrix formed using th …

A unimodular matrix $M$ is a square integer matrix having determinant $+1$ or $−1$. A totally unimodular matrix (TU matrix) is a matrix for which every square non-singular submatr …

I have a real supermodular objective function which I want to maximize with constraint. The constraint is on the size, like |A|=k . I am wondering if anyone can give me more inf …

Let $S_1,\ldots,S_m\subseteq U$ be subsets of a set $U$ of size $\lvert U\rvert=n$. Over all permutations $\pi$ of the set $\{1,\ldots,m\}$, I want to maximize the quantity \begin …

I have an optimization problem where I need to select $k$ integers over the interval $[0, N]$ s.t. I maximize the minimum difference between any pairwise sum of the $k$ integers (w …

Consider a set of $n$ real-valued number pairs: $(x_1,y_1), (x_2,y_2), \dots, (x_n,y_n)$. I want to find a permutation $p$ of the indices which minimizes the sum of consecutive a …

I need to find a Chinese postman circuit in a bidirected graph. Bidirected graph here is not the symmetric directed graph, but the graph introduced by Edmonds & Johnson in 19 …

Is there any suggestion about how could one construct a model that uses semidefinite programming that minimizes sum of k smallest eigenvalues of Laplacian matrix? I found two paper …

Suppose I am a high-volume broker aiming to make some money on a state lottery. In this lottery, six balls are drawn from a population of (let's say) 50, without replacement. A t …

I have a directed graph with edges connecting nodes representing costs. I wish to find the set of paths which -go from node 'start' to node 'end' -are node-disjoint (except for t …

Sorry, this is going to be technical and dirty. I am not looking for a proof of the Edmonds-Gallai structure theorem (I understand two of them, even if they are rather similar); I …

What is known about the following problem? Problem: Given an undirected, connected, planar graph $(V,E)$ with positive edge weights $q: E \to \mathbb{R}_0^+$, and given two distin …

let $A=\{1,2,3...,N\}$ and $B_1,B_2,B_3\dots,B_n$ be a series of subsets of $A$ which satisfied that $|B_i|=m$, $|B_i\cap B_j|\le k$. what is the maximum of $n$? ($k< m< N$) …

Let $z_1,z_2,\dots,z_N$ be vectors from $\mathbb Z^m$ for some $m$. The problem is: Given a positive integer $p$, find the subset $A_p \subset \{ 1,2,\dots,N \}$ of size $|A_p| = …

I was wondering if anyone here could give me any pointers as to how to solve the following problem. Let $B=(L,R,E)$ be a bipartite graph, and $\forall u\in L\cup R$, let $c_u$ be …