Problem Solving II - Distributed Software Develop - Slides | CS 682, Study notes of Software Engineering

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Distributed Software Development^ Problem Solving II

Chris BrooksDepartment of Computer ScienceUniversity of San Francisco^ Department of Computer Science — University of San Francisco – p.1/

17-0:^ Distributed Problem Solving

Last week, we talked about

loosely coupled

distributed

problems^ Primarily distributed search A large data set is divided across clients. Clients interact only with a central server; no client-clientcommunication

Department of Computer Science — University of San Francisco – p.2/

17-2:^ Example: scheduling classes

Before the semester starts, Wolber sends every teacheran email: When and where do you want your classes? Each professor has their own constraints, and can comeup with choices locally:^ Brooks: no classes before 10 am, in Kudlick^ Wolber: No classes on Friday^ Galles: Mornings, nothing on Lone Mountain. Brooks is able to eliminate some possible scheduleswithout consulting with anyone else.

Department of Computer Science — University of San Francisco – p.4/

17-3:^ Example: scheduling classes

Some choices require communication with a center(Wolber)^ Only one class in Kudlick at a time.^ Some classes may be constrained by otherdepartments’ choices^ CS 110 and Calculus I should be at different times. Nodes start with a large set of constraints; some areeliminated by the center. Hopefully at least one viable schedule remains.^ If not, someone is “encouraged” to relax theirconstraints.

Department of Computer Science — University of San Francisco – p.5/

17-5:^ Constraint Satisfaction

More formally, a CSP consists of:^ a set of variables

{x, x, ..., x}^12 n Each variable as a domain of possible values D, D, ..., D^12 n and a set of constraints

C, C, ...^12

Unary constraints:

x <^10 , ymod2 == 0

, etc Binary constraints:

x < y, x^ +^ y <

50 ,^ etc N-ary constraints:

x+^ x+^ ...^ +^1

x= 75n^ (a problem with N-ary constraints can betransformed into a binary constraint problem, with anincrease in the number of variables)

Department of Computer Science — University of San Francisco – p.7/

17-6:^ Formalizing a CSP

An assignment of values to variables that satisfies allconstraints is called a

consistent^ solution. We might might also have an objective function y^ =^ f^ (x, ..., x^1 n

)^ that lets us compare solutions.

Department of Computer Science — University of San Francisco – p.8/

17-8:^ Solving CSPs with search

We can use depth-first search to solve a CSP^ Begin with an initial state: no values assigned to^ x, ..., x^1 n^ Sequentially assign values to variables.^ We are done if we find an assignment to each variablesuch that all constraints are met. Since CSPs are commutative (for a solution, it doesn’tmatter which order values are assigned) we can considerone variable at a time.

Department of Computer Science — University of San Francisco – p.10/

17-9:^ Backtracking

With CSPs, the challenge is deciding how to proceedwhen a constraint is violated.^ Some assignment of values to variables must beundone, but which?^ This decision is called

backtracking Standard DFS undoes the most recently assignedvalue. This is called^ chronological backtracking Easy to implement Problem: an early assignment may have doomed us toan inconsistent solution.

Department of Computer Science — University of San Francisco – p.11/

17-11:^ Distributed CSP

In some cases, the variables in a CSP may be distributedover multiple nodes or processes or agents.^ Natural division of problem (e.g. scheduling a meeting,coordinating research teams)^ Information may be private, or difficult to quantify andshare. Constraints may be intra-agent or inter-agent. Agents communicate by message passing withasynchronous communication.

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17-12:^ Algorithms for Distributed CSP

For purposes of demonstration, we’ll make the followingassumptions:^ Each process has a single variable^ All variables have binary values^ All constraints are binary. Note: this is just to keep the examples simple; thealgorithms work fine without these assumptions.

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17-14:^ Asynchronous Backtracking

Example

x^

x2 !=!= x {1,2}^

{2} {1,2}

x1 and x3 can be either 1or 2. x2 can only be 2. x1 != x3, x2 != x3 (we can see that the onlysolution is x1 = x2 = 2, x3= 1)^ Department of Computer Science — University of San Francisco – p.16/

17-15:^ Asynchronous Backtracking

Example

Each node sends messages to other nodes that it sharesa constraint with.^ Includes all known assignments For example, x1 sends an

(ok?,^ (x^1 ,^ 1))^ to x3. x2 sends^ (ok?,

(x^2 ,^ 2))^ to x3. x3 constructs a

local view^ from this:

((x^1 ,^ 1),^ (x^2 ,^ 2)) x3 cannot choose a value consistent with this local view.

Department of Computer Science — University of San Francisco – p.17/

17-17:^ Asynchronous Backtracking

Example

x1 returns^ (x^1 ,

1), which x2 adds to its local view. x2 checks its current assignment and its local view againstthe list of nogoods.^ ((x^1 ,^ 1),^ (x^2

,^ 2))^ is a nogood. Therefore, x2, can’t find a consistent value, and so itsends^ (nogood,

(x^1 ,^ 1))^ back to x1. x1 receives the nogood. Since there are no otherprocesses included, x1 knows that it must change itsvalue. It chooses^ (x^1 ,^ 2)^ and resends

(ok?,^ (x^1 ,^ 1))^ to x2 and x3. x2 can safely also choose 2. When x3 gets the message,it sends^ (ok?,^ (

x^1 ,^ 2),^ (x^3 ,^ 2))^ to x2.

Department of Computer Science — University of San Francisco – p.19/

17-18:^ Asynchronous backtracking

Guaranteed to terminate and find a solution if one exists(complete). Same process as single-processor backtracking If an variable can’t be assigned a value, undo thenext-most-recent variable. More communication, due to asynchronicity.

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