network-flow

Linear Programming - Google ortools - incorrect decision variable final values

由 拜拜、爱过 提交于 2020-04-11 07:52:09
问题 I am trying to solve a linear programming problem. Following are specs of the problem: I have a network flow problem that's been converted to a linear programming problem. So, all the flow constraints, such as capacity, flow conservation etc., will have to be enforced. My objective is to minimize cost. Decision Variables - I have built two 8x8 matrices by defining a dictionary and adding decision variable at each of those 128 locations. Constraints - there are in total 24 constraints, namely:

How to find the maximum flow in a multi source flow network?

由 旧时模样 提交于 2019-12-24 18:50:55
问题 How to convert this multi source flow network in to single source flow network and find the maximum flow in that? 回答1: You create a dummy source node, called Source , and draw a directed edge of close-to-infinite-capacity (e.g. sum of capacities of all edges of the graph) from Source to each tank. Every flow in the resulting graph is in one-to-one correspondence with the original multi-source graph. 来源： https://stackoverflow.com/questions/51009304/how-to-find-the-maximum-flow-in-a-multi

Modification to Maximum Flow Algorithm

由 旧巷老猫 提交于 2019-12-21 04:57:20
问题 I've tried to solve a question about the maximum-flow problem. I have one source and two sinks. I need to find a maximum flow in this network. This part is general max-flow. However, both targets have to get same amount of flow in this special version of the max-flow problem. Is there anyone who can help me what should I do to do that? 回答1: Let s be your source vertex and t1 and t2 the two sinks. You can use the following algorithm: Use regular max-flow with two sinks, for example by

Minimum Cost Flow - network optimization in R

由 ℡╲_俬逩灬. 提交于 2019-12-19 04:04:16
问题 I am trying to implement a "Minimum Cost Network Flow" transportation problem solution in R . I understand that this could be implemented from scratch using something like lpSolve . However, I see that there is a convenient igraph implementation for "Maximum Flow". Such a pre-existing solution would be a lot more convenient, but I can't find an equivalent function for Minimum Cost. Is there an igraph function that calculates Minimum Cost Network Flow solutions, or is there a way to apply the

Find all edges in min-cut

由 。_饼干妹妹 提交于 2019-12-11 10:20:08
问题 Let (G,s,t,{c}) be a flow network, and let F be the set of all edges e for which there exists at least one minimum cut (A,B) such that e goes from A to B. Give a polynomial time algorithm that finds all edges in F. NOTE: So far I know I need to run Ford-Fulkerson so each edges has a flow. Furthermore I know for all edges in F, the flow f(e) = c(e). However not all edges in a graph G which respects that constraint will be in a min-cut. I am stuck here. 回答1: Suppose you have computed a max flow

All pair Maximum Flow

由 坚强是说给别人听的谎言 提交于 2019-12-10 03:09:12
问题 Given a directed weighted graph, how to find the Maximum Flow ( or Minimum Edge Cut ) between all pairs of vertices. The naive approach is simply to call a Max Flow algorithm like Dinic's, whose complexity is O((V^2)*E) , for each pair. Hence for all pairs it is O((V^4)*E) . Is it possible to reduce the complexity to O((V^3)*E) or to O(V^3) by some optimizations? 回答1: Gomory-Hu Tree does not work with directed graphs , putting that aside, Gomory-Hu Tree will form a Graph maximum flow by

All pair Maximum Flow

由 六眼飞鱼酱① 提交于 2019-12-05 03:51:50
Given a directed weighted graph, how to find the Maximum Flow ( or Minimum Edge Cut ) between all pairs of vertices. The naive approach is simply to call a Max Flow algorithm like Dinic's, whose complexity is O((V^2)*E) , for each pair. Hence for all pairs it is O((V^4)*E) . Is it possible to reduce the complexity to O((V^3)*E) or to O(V^3) by some optimizations? Gomory-Hu Tree does not work with directed graphs , putting that aside, Gomory-Hu Tree will form a Graph maximum flow by applying minimum cuts. The time complexity is: O(|V|-1 * T(minimum-cut)) = O(|V|-1 * O(2|V|-2)) ~ O(|V|^2) *

Modification to Maximum Flow Algorithm

由 此生再无相见时 提交于 2019-12-03 15:08:40
I've tried to solve a question about the maximum-flow problem . I have one source and two sinks. I need to find a maximum flow in this network. This part is general max-flow. However, both targets have to get same amount of flow in this special version of the max-flow problem. Is there anyone who can help me what should I do to do that? Let s be your source vertex and t1 and t2 the two sinks. You can use the following algorithm: Use regular max-flow with two sinks, for example by connecting t1 and t2 to a super-sink via edges with infinite capacities. You now have the solution with maximum

Minimum Cost Flow - network optimization in R

由 元气小坏坏 提交于 2019-11-30 23:52:08
I am trying to implement a " Minimum Cost Network Flow " transportation problem solution in R . I understand that this could be implemented from scratch using something like lpSolve . However, I see that there is a convenient igraph implementation for " Maximum Flow ". Such a pre-existing solution would be a lot more convenient, but I can't find an equivalent function for Minimum Cost. Is there an igraph function that calculates Minimum Cost Network Flow solutions, or is there a way to apply the igraph::max_flow function to a Minimum Cost problem? igraph network example: library(tidyverse)

What exactly is augmenting path?

由 南楼画角 提交于 2019-11-29 02:08:03
问题 When talking about computing network flows , the Algorithm Design Manual says: Traditional network flow algorithms are based on the idea of augmenting paths , and repeatedly finding a path of positive capacity from s to t and adding it to the flow. It can be shown that the flow through a network is optimal if and only if it contains no augmenting path. I don't understand what is augmenting paths . I have googled, and found: Augmenting Path in Wolfram Flow network in Wiki but they all
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