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4 votes
2 answers
314 views

Connecting $2n$ points in $\mathbb R^2$ with line segments s.t. each point belongs to exactly one line segment

I'm trying to do a certain simulation related to the toric code and I'm looking for an algorithm that connects $2n$ points ($n \in \mathbb Z_+$) in $\mathbb R^2$ with line segments with the following ...
Sanchayan Dutta's user avatar
0 votes
0 answers
40 views

Subtour-gluing constraints for ILP formulation of TSPs

If one doesn't want to introduce additional variables to the ILP of a TSP instance, one has to add exponentially many so-called subtour-elimination constraints; in practical calculations subtour-...
Manfred Weis's user avatar
  • 13.2k
0 votes
1 answer
76 views

A question on graph partitioning

Given a connected un-directed simple graph $G=(V,E)$, is there a polynomial time algorithm to find the smallest subset $S$ of $V$ such that each node in $V \setminus S$ has at least 50% of its ...
DSM's user avatar
  • 1,216
0 votes
0 answers
99 views

Is this Graph Iteration Already Known?

When attempting to set up an ILP formulation for a weight-minimal cubic spanning tree (i.e. one with vertex degrees either 1 or 3) I needed connectivity constraint, but misremembered the contents of ...
Manfred Weis's user avatar
  • 13.2k
2 votes
1 answer
3k views

max-flow at max-cost

I have a flow network with gains. In practical terms, a gain is the opposite of a cost. So, I interested in finding the maximal gain of a network flow, what could be interpreted as finding a maximum ...
lrleon's user avatar
  • 121
2 votes
1 answer
426 views

Network flows with shared capacities

Suppose we have a flow network, with capacity constraints on weighted sums of arc flows, such as: $$2 f(1, 2) + 3 f(4, 5) + f(3, 7) \leq 10,$$ where $f(1, 2)$ denotes the flow through arc $(1, 2)$....
robertdg's user avatar