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2
votes
1answer
122 views

Can the optimal minimum cost two-commodities flow be fractional on this special case?

Suppose that we have a two commodities flow network $N=<G=(V,E), s_1,s_2,t_1,t_2\in V>$. The problem is to find a minimum cost two-commodity flow in which there a flow $f_1$ from $s_1$ to $t_1$ ...
0
votes
1answer
276 views

Maximum matching versus preferential assignment

There are several ways to solve the marriage problem. The "preferential assignment" approach consists in forming couples on the basis of preferred characteristics expressed by each individual. An ...
3
votes
0answers
75 views

another solution problem (ASP) of integer multicommodity flow: is it NP-complete?

I know that integer multicommodity flow is NP-complete. It was proven in "On the complexity of time table and multi-commodity flow problems" (http://dl.acm.org/citation.cfm?id=1382492) that any SAT ...
2
votes
0answers
40 views

Approximating BLEDP on restricted graph classes

In the edge-disjoint paths (EDP) problem, we are given an undirected graph $G$, and a set $\{ (s_i,t_i) \mid 1 \leq i \leq k \}$ of $k$ source-sink pairs. The objective is to maximize the number of ...
3
votes
1answer
168 views

How can we derive this lower bound of a special cut in a graph?

I have another question about this paper. There the authors prove a special version of the maximal flow-minimal cut theorem for uniform exactly-$k$-splittable $s$-$t$-flows. They define the cut in ...
5
votes
1answer
183 views

Finding the perfomance ratio in a multicommodity-flow

I am reading the following paper about multicommodity-flows. I have not a very strong background in graph theory and hence most of my question regarding the paper are fundamental. My questions are ...
5
votes
0answers
188 views

On the optimal solution of the CKR formulation for MULTIWAY CUT

Currently the best approximation algorithm for the MULTIWAY CUT problem is obtained via the linear program based on geometrical embedding by CKR [1]. Let $U_i$ be those vertices in $V-T$ which is ...
8
votes
1answer
210 views

Request for references on multicommodity flow-cut results

This is a somewhat subjective question. I am interested in studying the literature on multicommodity flow-cut results, especially the 'positive' results which show that flow is a good approximation to ...
6
votes
1answer
185 views

multi-commodity flow acyclic digraphs

I am faced with the following question on max. integer multiflow: INSTANCE: An acyclic directed graph G=(V,E), a capacity function c:E→N, k pairs of vertices (si,ti) and a demand function ...
5
votes
1answer
389 views

On the faces of the multicommodity flow polytope

Consider the multicommodity flow problem on an undirected graph with k source-destination pairs and specified capacity constraints on the edges. The set of concurrently achievable flows ...