Commit fbad515c authored by Christopher Alfeld's avatar Christopher Alfeld
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Big brain dump of text, info, and thoughts about assign.

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Interesting things about Assign
This document is not meant to be a cohesive whole. Rather a brain
dump of text, thoughts, and information.
Solutions in assign are measured by two criteria. The first
is a measure of basic quality, very similar to the cost
functions you would find in traditional SA. The second is a
measure of validity. It is an integer recording the number of
violations, or broken constraints. By allowing invalid states
the SA algorithm can traverse non-solution space to find other
solutions. Having two separate measures allows find tuning of
the SA algorithm. In particular it allows us to control the
tendency to wander into non-solution space. A secondary
advantage is that by tracking the source of each violation it
is easy to understand the cases where assign fails to find a
valid solution.
The basic problem is to map one graph to another. It is not,
however, simply a matter of connecting up vnodes and pnodes
and vlinks and plinks. Multiple vnodes may map to a single
pnodes, as is the case with delay nodes. Links are even more
complicated. Certain plinks, such as interswitch trunks, may
have multiple vlinks mapped to them. On the other hand, each
vlink will probably traverse multiple plinks. It is quite
often that a vlink will map to multiple plinks, some of which
have other vlinks mapped to them. These many-to-one and
one-to-many relationships complicate scoring and
Further complications arise from the many criteria that
solutions are judged by. How well vnodes and pnodes match,
the feasibility of emulating vlinks, the "cheapness" of all
resources used, are some of the basic criteria. In addition a
solution is based on how well it satisfies specific requests,
such as that a node already have the correct disk image
installed. The "cheapness" of nods is not straight forward, a
node with specialized hardware should be more expensive than
its non specialized counterparts, yet that expense should only
be considered if the hardware would not be used. Assign also
optimizes for node homogeneity, both at a general physical
level, and according to logical classification of vnodes by
the user. All of these criteria have various priorities and
interact with each other during the algorithm.
Given the complexity of the scoring and the vast number of
times the score will be recalculated during a run it is
infeasible to calculate the score from scratch at each
modification. Instead, the change in the score needs to be
rapidly calculated.
The two basic operations in assign are mapping a vnode to a
pnode and unmapping a vnode from its pnode. At each operation
the change in score (both quality and violations) is
calculated and applied. The change in score is non-trivial
and highly depends on the state of the other nodes and links.
Mapping a vnode requires an evaluation of how well it maps to
the chosen pnode; the choice and evaluation of any links the
vnode might have that connect to mapped vnodes (vlinks are
only evaluated when both ends are mapped), possibly involving
the allocation of one or more switches; the new physical
homogeneity of pnode usage; and the consistency of any vclass
the vnode might be in. All of these need to be evaluated,
even under conditions in which the current state is invalid.
For example, mapping a node may require over utilizing a link.
The score still needs to be updated, and needs be updated to
reflect the over-utilization (an increase in the number of
The mapping of a vnode and the later unmapping of a vnode will
not necessarily result in opposite effects on the score (in
fact, it is very rare that they do so). For between map and
unmap a number of other changes have been applied, each of
which depended on the fact the vnode was mapped. Unmapping
the vnode needs to reflect those dependencies and modify the
score and state appropriately. As an example, a vnode may be
mapped, and later on one of its neighbors mapped. Mapping
that neighbor in will cause the link between them to be
evaluated. When the original node is unmapped the effect of
that evaluation must be undone.
Assign has a detailed resource availability and use model.
Each pnode has a number of resources along with their values.
The value reflects the cost of the resource in the case that
the resource is allocated but unused. For example, a pnode
may have specialized hardware. If that pnode is allocated as
part of a solution but the vnode will not use that hardware,
then the cost is included in the score. Vnodes have resource
requests along with the cost of having that request
unfulfilled. Besides a quality modification, an unfulfilled
request can, at the users discretion, result in an increase in
violations. This basic mechanism of features and desires
allows a wide range of control over the nature of any
Assign has a notion of physical equivalence classes. Pnodes
are grouped together in cases where the choice of either pnode
will have no effect on the score. The simulated annealing
then chooses among pclasses instead of pnodes, dramatically
reducing the scaling properties. The idea and tracking a
pnodes is still very important, as even within a pclass,
pnodes may differ in the vnodes mapped to them, specifically
as multiple vnodes can map to a single pnode. Thus not only
must assign look at pclasses but also within, at what
partially full pnodes are available. By using simulated
annealing on pclasses and heuristics to choose among the
members of a pclass, assign finds middle ground between nodes
and equivalence classes.
Assign must be able to handle partial solutions specified as
input. This is important in cases where users require a
specific machine for reasons outside the knowledge of assign.
It also provides opportunities to strongly influence a
solution. For example in a distributed testbed, a local node
could be fixed causing solutions to tend to utilize nearby
nodes. Without, the pnodes could very well be on the far end
of a continent or beyond.
Often the user will be aware of relations among their vnodes
that assign does not otherwise have the knowledge to be aware
of. For example, a user may put great important on the
homogeneity of internal nodes vs. leaf nodes, but care little
as to whether leaf and internal are similar. Vtypes allows
the user to specify these relationships to assign. The
challenge to assign is to deal with these vnodes that are not
restricted to a single type but are requested to match in type
to other vnodes. The user is allowed to specify the
importance of the consistency, anywhere from negligible to
invalidating any solution with inconsistency within a vtype.
Even in the latter case, however, assign allows for
inconsistent solutions, keeping track of the violations.
Before beginning simulated annealing assign performs a number
of checks and computations to improve performance and avoid
pathological cases that are obvious to heuristics but not SA.
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