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Algorithms: minimum route coverage in a directed acyclic graph

Given a weighted directed acyclic graph G = (V, D, W) and a set of arches RE & # 39; of rewhere the weights of W They are at the vertices. The problem is partitioning Sun on a minimum number of paths separated from vertices that cover all vertices of Sun subject to restrictions that:

  1. the weight of each route is maximum k.
  2. each route must include at least one edge of D & # 39;

What is the complexity of this problem?

Longer trajectory in an acyclic graph directed with restrictions

Given a directed weighted acyclic graph G = (V, D, W) and a subset of edges RE & # 39; of re. The problem is finding the longest path in Sun that goes through exactly one edge of RE & # 39;.

What is the complexity of this problem?

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algorithms: extraction of an expansion tree from a directed acyclic graph with a minimum total distance between terminal nodes

I have a directed acyclic graph that has uniform edge weights. I would like to extract from this graph an expansion tree (an arborescence) with the property that the total distance between all pairs of leaf nodes (the sum of the combined distances of the closest common ancestor of each pair) is minimized.

What I am finally trying to achieve is finding the best way to sort the leaf nodes so that the most related nodes are closer to each other on the list. If I can find the expansion tree as described, I can easily sort the leaf nodes the way I need.

Can anyone point me to a solution to this problem that is not just brute force optimization?

Wi-Fi: Do modern operating systems still send requests for targeted or directed Wi-Fi probes that contain SSID?

Do modern operating systems (versions of), mainly Android and iOS on mobile devices, still send directed or directed polling requests when they search for Wi-Fi networks to connect?

Such directed or directed polling requests contain the SSIDs of known networks and, therefore, can filter information about the location history of the sending device, the owner's social relations, etc.

According to this source, modern operating systems no longer send these requests:

Around 2014, the privacy implications of targeted polling requests began to be widely publicized and understood. Therefore, most new devices stopped sending them. (…) When the privacy implications of the targeted request probes became widely appreciated, most new mobile devices stopped sending them completely. (…) Targeted polling requests are mostly from the past.

Other sources, such as this or this one, seem to confirm that specific polling requests are no longer sent in the latest Android versions, at least.

If this is true, and perhaps also for iOS (and some desktop OS), are there any press releases, bug tracker entries, security reports or code confirmations that confirm it?

Targeted polling requests, unlike broadcast requests that do not contain the SSID of a network, should only be necessary for hidden networks. The impact is stronger on mobile devices, where they tend to have more known networks added to their device and transmit that list in more places.

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np complete – HAMCYCLE NOT DIRECTED to HAMPATH reduction

I will define the problems


Input: A non-directed graph G and 2 nodes, syt

Question: Is there a Hamiltonian path from s to t in G?


Input: a non-directed graph G

Question: Is there a Hamiltonian cycle in G?


my reduction is as follows $ (G) a (G & # 39 ;, s, t) $


    for each e = (u, v) in E(G)
        G' = G
        add nodes u' and v' to G'
        add edges (u', u) and (v, v')
        s = u'
        t = v'
        if there is a hamilton path from s to t:
            return (G', s, t)

Basically, if there is a hamilton cycle in G, then some edge in $ G $ will form a Hamilton road in $ G & # 39; $.

An example to further illustrate the reduction:

 Graph G

(a) ---- --(d)
 |         |
 |         |
 |         |
 |         | 
 |         | 
 |         |
 |         |      |
(b) ------ (c)

Has a clear Hamilton cycle (a, b, c, d). 

If we choose edges (a, d)

 Graph G'

(s)--(a) ---- --(d)
      |         |
      |         |
      |         |
      |         | 
      |         | 
      |         |
      |         |      
     (b) ------ (c)--(t)

It doesn't have a hamilton path from s to t. However, if you choose any other advantage such as (a, d), then

(s)--(a) ---- --(d)--(t)
      |         |
      |         |
      |         |
      |         | 
      |         | 
      |         |
      |         |      
     (b) ------ (c)

$ (s a a to b to c to d to t) $. Wait.

I am confused if I can use this line or not:

if there is a hamilton path from s to t:
    return (G', s, t)

Checking if a graph has a hamilton path is NP complete, but as we are trying to reduce it, I think we can.