postgresql – Postgres 11+: are coverage rates (INCLUDE) useful for joining conditions / where?

I would like to better understand when covering indexes can be useful to make possible single-index scans in Postgres 11+. As the documentation says, given the coverage rate

CREATE INDEX tab_x_y ON tab(x) INCLUDE (y);

queries like this can use it for single index scans:

SELECT y FROM tab WHERE x = 'key';

Now I wonder if such coverage index could also allow single index scans when coverage columns appear as conditions. For example, assume a coverage index:

CREATE INDEX tab_x_y_z ON tab(x) INCLUDE (y, z);

Would this allow single index scans for subsequent queries?

SELECT z FROM tab WHERE x = 'key' AND y = 1;

SELECT x, y, z FROM (VALUES ('key1'),('key2'),('key3')) sub(id)
JOIN tab ON tab.x = sub.id WHERE y = 1;

United States: insurance coverage needed by Canadians visiting the United States

My brother, in his seventies, hopes to visit a relative in Arizona for about two weeks in June. He has had multiple bypass surgeries. There are no other significant ailments. What types and levels of coverage should I have?

  • hospitalization, doctors, nurses, etc.
  • air ambulance at home
  • Arizona ambulance.

Other elements? Figures in dollars?

Thank you!

Do "excluded coverage pages" cause the rank drop in Google search result?

I don't understand what is causing the drop in range, but these figures may be something I have to look at. Do I have to worry about those excluded pages or leave them as they are?

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Algorithms: minimum vertex coverage to access k edges

I need to find the minimum number of N vertices in a tree with N-1 edges, so that at least K edges of that tree are connected to these vertices.

For example, if N = 9 and K = 6 and we have this tree:

   Edges  |  Vertice #1  | Vertice #2
     1            1          2
     2            1          3
     3            1          4
     4            2          5
     5            2          6
     6            3          7
     7            4          8
     8            4          9

The correct answer should be min = 2.

Any ideas?

graphics – Derandomization of the vertex coverage algorithm

I have the following random algorithm for the vertex cover problem. Leave $ B_0 $ be the output set:

Fix some order $ e_1, e_2, …, e_m $ over all the edges in the set of edges E of G, and set $ B_0 = ∅ $.

Add $ B_0 $ all isolated vertices, that is, those that have no incident edges.

For each edge $ e $ in $ e_1, e_2, …, e_m $
if both ends of e are not contained in $ B_0 $, then
throw a fair coin to decide which of the endpoints to choose and add this endpoint to $ B_0 $.

I have already shown that this algorithm has $ E [| B_0 |] le 2 | OPT | $.

Now I do not know how to apply the method of conditional expectations to derandomize the algorithm in order to demonstrate that we cannot obtain an efficient deterministic version and that it gives the same result of the expected value found above.
Can you teach me how to do this?

smooth collectors – Question about the partition ratio of the unit subordinated to a coverage and extrusion function

So I was just reading about the relief function and I realized that they always seem to be relevant when we consider that the unit partitions are subordinate to an open cover.

The definition of the partition of the unit subordinated to an open cover:

Yes $ {U_i } _ {i en I} $ it is a finite open cover of $ M $, a $ C ^ infty $
partition of the unit subordinate to $ {U_i } $ It is a collection of
not negative $ C ^ infty $ functions $ { rho_i } _ {i in I} $ satisfactory

(a) $ sum rho_i = 1 $;
(yes) $ operatorname {supp} rho_i ⊂ U $

My question is: How does this relate exactly to the relief functions? I know a hit function $ f $ it is a compatible compact function that is $ f equiv 1 $ in its compact support and rapidly decreases s.t. is $ f equiv 0 $ Outside a compact neighborhood of your support.

Because the way I imagine relief functions (as a tool) is that sometimes we could use several relief functions in different neighborhoods of local coordinates of the same variety $ M $. However, if that is the case, I do not see how condition (a) is maintained from above.

Maybe I imagine it completely wrong?

Thank you very much for any clarification.

graphics: maximum coverage version of the dominant set

The dominant problem is:

Given a $ n $ vertex graph $ G = (V, E) $, find a set $ S ( subseteq V) $ such that $ | N (S) | $ is exactly $ n $, where $$ N (S): = {x ~ | text {$ $ $ or a neighbor of $ x $ is in $ S $} } $$

My question is whether the following (new problem) has a definite name in the literature, and if not, what should be the most appropriate name.

New problem: Given a $ n $ vertex graph $ G = (V, E) $ and an integer $ k $ , find a set $ S ( subseteq V) $ of size $ k $ such that $ | N (S) | $ It is maximized.

For the second problem, some of the names I've seen in the literature are maximum graphics coverage; partial coverage; k-dominating-set, (however, the exact same names are also used in other contexts).

general topology: reverse image of the subspace connected to the route below a coverage map

I have the following question:

Assume $ p: widetilde {X} a X $ it's a coverage map with $ widetilde {X}, X $ both connected to the route. Assume $ A $ is a subset of connected path of $ X $ so that $ i _ *: pi_1 (A, a) to pi_1 (X, a) $ it's for some $ a in A $ where $ i $ It is the inclusion map. Test it $ p -1 (A) $ It is the connected road.

I realize that this question has been asked in this post if $ p: widetilde {X} rightarrow X $ is a coverage space and $ widetilde {X} $ is connected, shows that $ p ^ {- 1 } (A) $ is the connected route. and users said the claim was false. However, in the question I have we have to $ i _ * $ It's about what seems to make it work. This is what I came up with:

leave $ a_1, a_2 in p ^ {- 1} (A) $. Consider the elements $ p (a_1), p (a_2) in A $. As $ A $ it's way connected there is a way $ f $ in $ A $ since $ p (a_1) $ to $ p (a_2) $. On the road that lifts the property, we can lift $ f $ one way $ tilde {f} $ from $ a_1 $ and ending somewhere in the fiber $ p -1 (a_2) $. Call this point $ a_3 $ (so $ tilde {f} $ it's a road in $ p -1 (A) $ since $ a_1 $ to $ a_3 $ where $ a_3 in p ^ 1 (A) $)

Now from $ widetilde {X} $ Road is connected, elevation correspondence is overjective. Therefore, there is some loop $ g $ based on $ p (a_3) $ in $ X $ such that the elevator $ tilde {g} $ it's a road in $ widetilde {X} $ since $ a_3 $ to $ a_2 $. Now from $ i _ * $ is in there is a loop $ h $ based on $ p (a_3) $ such that $ i circ h $ it's homotopic to $ g $. For the homotopy elevation property, $ widetilde {i circ h} $ it's a road in $ widetilde {X} $ that starts at $ a_2 $ and ends in $ a_3 $. This means that $ tilde {h} $ it's a road in $ p -1 (A) $ since $ a_3 $ to $ a_2 $ (I'm not sure if this follows so directly from what I said). Then, $ tilde {f} cdot tilde {h} $ it's a road in $ p -1 (A) $ since $ a_1 $ to $ a_2 $.

Does the above argument seem to make sense? Any comments or suggestions would be helpful.

The "View coverage index" link on the site map does not work in the Google Search Console (I cannot click)

During the last week, I had this problem in the Google search console. The "see coverage index" link does not work. I can't click on it to see the index and the URLs sent on the site map.

I tried to resubmit the site map to all versions, but it still doesn't work.

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random charts: I can't understand the coverage of randomized vertices

I am studying this article: in section 11.3 talk about the randomized vertex cover saying that it is at most 2 times the optimal vertex cover. That doesn't sound to me because if I have a graph with borders {{1,2}, {1,3}, {1,4}} (edges of xay and vice versa) the optimal vertex coverage would be (1) (node ​​1) . Using the random algorithm, it would be possible to have a vertex cover (2,3,4) that is 3 times the optimal solution and not 2 (adding more edges can be even worse)
What have i lost?