September 12, 2005 CSP 101: continued 1 Foundations of Constraint Processing, Fall 2005 Foundations of Constraint Processing CSCE421/821, Fall 2005: www.cse.unl.edu/~choueiry/F05-421-821/ Berthe Y. Choueiry (Shu-we-ri) Avery Hall, Room 123B [email protected]Tel: +1(402)472-5444 Constraint Satisfaction 101
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Foundations of Constraint Processing, Fall 2005 September 12, 2005CSP 101: continued1 Foundations of Constraint Processing CSCE421/821, Fall 2005: choueiry/F05-421-821
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• Semi-complete: At least one solution is kept• Complete: No solution is lost
• Redundant: Solutions replicated in { Pi}
• Reducible: may be < Size( P)
September 12, 2005 CSP 101: continued 6
Foundations of Constraint Processing, Fall 2005
Deep analysis
Uncover particular properties, e.g.– bound the required level of consistency (islands of tractability)– predict ease/difficulty of solving a given instance
• Structure, topology of the constraint graph– tree, DAGs, chordal, bounded-width/induced width, k-trees, etc.
• Types, semantics of the constraints– linear inequalities, subsets of Allen's relations, functional,
monotonic, row-convex, all-diffs, etc.
• Order parameter (phase transition)
September 12, 2005 CSP 101: continued 7
Foundations of Constraint Processing, Fall 2005
Phase transition [Cheeseman et al. ‘91]
Cos
t of
sol
ving
Mostly solvable problems
Mostly un-solvable problems
Order parameterCritical value of order parameter
• Significant increase of cost around critical value• In CSPs, order parameter is constraint tightness & ratio
• Algorithms compared around phase transition
September 12, 2005 CSP 101: continued 8
Foundations of Constraint Processing, Fall 2005
Distributed CSPs• Mainly in search
– Asynchronous BT (e.g., work of Yokoo)– Fine grain local search (ERA, by Liu)– Privacy of constraints
• More purist multi-agent approaches– In scheduling & resource allocation– Based on decomposition of problem/solvers
• Let’s take a wider perspective than what is done today…
September 12, 2005 CSP 101: continued 9
Foundations of Constraint Processing, Fall 2005
Multi agent approach1. Computational tasks:
problem decomposed, replicated
2. Types of agent:broker, solver, problem, solver+problem
3. Architecture and authority:hierarchical, egalitarian, priority-based (e.g., vote)
4. Nature of communication:agent-to-agent, group, broadcast
5. Interaction strategies: cooperating vs. competing
transparent vs. secretivenegotiation + alliance/coalition formation
September 12, 2005 CSP 101: continued 10
Foundations of Constraint Processing, Fall 2005
Computational tasks• At one end of the spectrum, agents may be involved in
solving heterogeneous, distinct and completely independent problems and request other agents to supply specific functionalities for the completion of the individual tasks.
• At the other end of the spectrum, the same problem could be replicated and assigned to all agents, which can then share their individual results with other agents incrementally in order to speed up the execution of the global computational task.
September 12, 2005 CSP 101: continued 11
Foundations of Constraint Processing, Fall 2005
Types of agentsAn agent in the system can be any of the following:
• an agent that collects data from the environment and formulates the CSP
• a reasoning module with specific computational characteristics (e.g., various search algorithms)
• brokers that facilitate matching between a service seeker and a number of service providers (e.g., CORBA brokers).
September 12, 2005 CSP 101: continued 12
Foundations of Constraint Processing, Fall 2005
Agent architecture..
.. and how authority is granted• Agents could be organized in a strict hierarchy in which
a given agent has full control over the activities of the agents that lie underneath it in the hierarchy. It decides how the lower level agents may cooperate while ensuring coordination with the higher-level agent.
• Agents could be in a strictly flat structure competing for services and rewards, either chaotically or according to some strict priority policy, for example, based on voting or time-responsiveness.
September 12, 2005 CSP 101: continued 13
Foundations of Constraint Processing, Fall 2005
Communication environment
Communications among agents may be conducted according to:
• a one-to-one schema
• multi-cast (i.e., one-to-group),
• or broadcast, where all agents in the environment have access to the content of the communicated information.
September 12, 2005 CSP 101: continued 14
Foundations of Constraint Processing, Fall 2005
Type of supported interactions
• Agents may be cooperative, pooling their resources and capabilities to achieve a common, global objective, or they could be competitive trying to win rewards and optimize their individual gain.
• They could also adopt a midway strategy, dynamically forming coalitions and gathering support to acquire more resources and realize greater gains.
• Also, agents may be transparent about their intentions, resources, needs, and constraints or may be secretive, hiding one or the other of their strengths or weaknesses.
September 12, 2005 CSP 101: continued 15
Foundations of Constraint Processing, Fall 2005
Outline
Advanced solving techniques
Issues & research directions
CSP in a nutshell
Constraint Logic Programming (quickly)
September 12, 2005 CSP 101: continued 16
Foundations of Constraint Processing, Fall 2005
Research directions• Preceding (i.e., search, backtrack, iterative repair, V/V/ordering,
consistency checking, decomposition, symmetries & interchangeability, deep analysis)
• Evaluation of algorithms– worst-case analysis vs. empirical studies– random problems vs. real-world problems