How to solve the minimum-cost flow problem on a complete graph, with a concave cost function of flow for each edge?

Here is the problem: Input: A series of source/sink nodes at fixed positions with given outwards/inwards flow Edges are NOT specified. The edges can connect any nodes. The total source and sink flow match A concave cost function that gives a cost per edge in terms of flow capacity Expected output: The minimum costing graph … Read more

How to compute all inequivalent (under Aut(P)) nonnegative integer weight assignments (with fixed sum) to the vertices of a finite poset P?

Let P be a poset on n points, Aut(P) its automorphism group, and a1,a2,…,ak the lengths of the orbits under Aut(P). Goal: An algorithm to generate a member from each equivalence class (under Aut(P)) of assignments of nonnegative integer weights to the vertices of P such that the weights sum to m. Partial result: My … Read more

Determining on whether topology is a tree or a hypercube

Assume that the nodes know that the topology G is either a hypercube or a tree. Assuming a unique initiator, design an algorithm to discover the topology. In other words, you would like a node to reach terminal state TREE if G is a tree, terminal state HYPERCUBE if instead it is a hypercube. Let … Read more

Analyzing the railways network [closed]

Closed. This question needs to be more focused. It is not currently accepting answers. Want to improve this question? Update the question so it focuses on one problem only by editing this post. Closed 2 years ago. Improve this question I am studying complex networks and I have a question. Is it possible to use … Read more

binary representation of ip prefixes

How does an ip prefix 90.0.0.0/4 translate to 0101∗ in binary and 10.0.0.0/2 to this: 00* I’m trying to understand it since a while now but I am unable to derive the logic. Answer For a netmasked IP address xxx.xxx.xxx.xxx/N, convert each xxx octet in the address to binary. The masked address is the leftmost … Read more

Which neural network topology is the most efficient to generate randomly shaped letters?

I have created some unique shapes, so-called “letters” for a custom alphabet, all of which can fit into 9×9 pixels. Instead of drawing countless more, I try to combine two solutions I saw in a relevant part of Reddit, and decided to let a neural network create some additional examples. Desconstructing the problem: letters are … Read more

What is the difference between broadcast and gossip/epidemics?

Everything is in the title. What is the difference between broadcast and gossip in the context of message-passing distributed systems? According to Wikipedia, gossip and epidemic protocols/epidemics are synonym. Thank you for your help. Answer While sometimes used as synonyms, to me, gossiping protocols are certain flavor of broadcast algorithms, where the message is flooded … Read more

What’s an example of a planar graph with two embeddings whose geometric duals are nonisomorphic?

How to prove that the dual of the dual of a connected planar graph G is isomorphic to G? In the post linked above, the user “plop” gives a great response where they claim, in particular, that a plane graph G has a well-defined geometric dual. Paraphrasing, for any two drawings G∗1 and G∗2 obtained … Read more