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updates from summit

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warner committed Nov 15, 2016
1 parent ae77df1 commit 7a46e6047df73372c558339ef8e008537df00422
Showing with 37 additions and 23 deletions.
  1. +37 −23 docs/specifications/servers-of-happiness.rst
@@ -194,39 +194,53 @@ Calculating Share Placements

We calculate share placement like so:

1. Query *2N* servers for existing shares.
0. Start with an ordered list of servers. Maybe *2N* of them.

2. Construct a bipartite graph of *readonly* servers to shares, where an edge
exists between an arbitrary readonly server S and an arbitrary share T if
and only if S currently holds T.
1. Query all servers for existing shares.

3. Calculate a maximum matching graph of that bipartite graph. There may be
more than one maximum matching for this graph; we choose one of them
arbitrarily.
2. Construct a bipartite graph G1 of *readonly* servers to pre-existing
shares, where an edge exists between an arbitrary readonly server S and an
arbitrary share T if and only if S currently holds T.

4. Construct a bipartite graph of servers (whether readonly or readwrite) to
shares, removing any servers and shares used in the maximum matching graph
from step 3. Let an edge exist between server S and share T if and only if
S already holds T.
3. Calculate a maximum matching graph of G1 (a set of S->T edges that has or
is-tied-for the highest "happiness score"). There is a clever efficient
algorithm for this, named "Ford-Fulkerson". There may be more than one
maximum matching for this graph; we choose one of them arbitrarily, but
prefer earlier servers. Call this particular placement M1. The placement
maps shares to servers, where each share appears at most once, and each
server appears at most once.

5. Calculate the maximum matching graph of the new graph.
4. Construct a bipartite graph G2 of readwrite servers to pre-existing
shares. Then remove any edge (from G2) that uses a server or a share found
in M1. Let an edge exist between server S and share T if and only if S
already holds T.

6. Construct a bipartite graph of servers (whether readonly or readwrite) to
share, removing any servers and shares used in the maximum matching graphs
from steps 3 and 5. Let an edge exist between server S and share T if and
only if S *could* hold T (i.e. S is readwrite and S has enough available
space to hold a share of at least T's size).
5. Calculate a maximum matching graph of G2, call this M2, again preferring
earlier servers.

7. Calculate the maximum matching graph of the new graph.
6. Construct a bipartite graph G3 of (only readwrite) servers to shares. Let
an edge exist between server S and share T if and only if S already has T,
or *could* hold T (i.e. S has enough available space to hold a share of at
least T's size). Then remove (from G3) any servers and shares used in M1
or M2 (note that we retain servers/shares that were in G1/G2 but *not* in
the M1/M2 subsets)

8. Renew the shares on their respective servers from steps 3 and 5.
7. Calculate a maximum matching graph of G3, call this M3, preferring earlier
servers. The final placement table is the union of M1+M2+M3.

9. Place share T on server S if an edge exists between S and T in the maximum
matching graph from step 7.
8. Renew the shares on their respective servers from M1 and M2.

10. If any placements from step 7 fail, remove the server from the set of
possible servers and regenerate the matchings. XXX go back to step 4?
9. Upload share T to server S if an edge exists between S and T in M3.

10. If any placements from step 9 fail, mark the server as read-only. Go back
to step 2 (since we may discover a server is/has-become read-only, or has
failed, during step 9).

Rationale (Step 4): when we see pre-existing shares on read-only servers, we
prefer to rely upon those (rather than the ones on read-write servers), so we
can maybe use the read-write servers for new shares. If we picked the
read-write server's share, then we couldn't re-use that server for new ones
(we only rely upon each server for one share, more or less).

Properties of Upload Strategy of Happiness
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