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Improving NEST Performance Using Surrogates C I R L David W. Etherington Andrew J. Parkes Matt Ginsberg Project Status: Dec 16, 2003 University of Oregon

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C I R L Administrative Project Title: Improving NEST Performance Using Surrogates Program Manager: Vijay Raghavan PI Names: David W. Etherington, Matthew L. Ginsberg, Andrew J. Parkes PI Phone Numbers: {0472, 0471, 0434} PI Addresses: {ether, ginsberg, Company/Institution: CIRL/University of Oregon Contract Number: F C-4032 AO Number: Award Start Date: 9/12/2002 Award End Date: 9/11/2005 Agent Name/Organization: Ed DePalma, AFRL

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C I R L Subcontractors and Collaborators Subcontractors –none Collaborators –none

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Problem and ChallengeNew Ideas FY04 Schedule Application of surrogates to distributed reasoning easy-to-measure standins for properties of interest Transition behaviors can be used to justify use of surrogates for system behavior prediction/control Extend notion of relaxation to approximate relaxations Explore the interaction between structure and transitions Improving NEST Performance Using Surrogates Avoidance of dangerous regions; develop tractable mechanisms for design/control/prediction Find manageable surrogates for critical properties 1QFY04 Demonstrate use of local surrogates in random NESTs Determine thresholds for static global surrogates 2QFY04 Discover local surrogates for static properties of interest Use static global surrogates to predict/control structured NESTs 3QFY04 Develop temporally structured NEST testbed/generator Determine thresholds for static local surrogates 4QFY04 Identify functional dynamic properties in temporally structured NESTs Use static local surrogates to predict/control structured NESTs Impact Simplified design and control of performance Simplified performance prediction/modeling with uncertain configuration information e.g., prediction of capabilities under various attrition/failure models Predict/determine maintenance/replenishment requirements under uncertain field conditions e.g., model tradeoffs of capabilities vs costs Q1Q2Q3Q4 Etherington, Parkes CIRL, University of Oregon cost quality approx- imation full property param estimation pure surrogates estimation + phase xition

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C I R L Problem Description/Objective Problem: NEST systems induce difficult design and control problems –these impair our ability to achieve expected benefits like robustness and speed Goal: develop the ability to predict, analyze, and bound NEST performance “in the large” Approach: use surrogates: properties that are easy to measure/control yet strongly correlated with real objectives –identify “hard” properties of interest –exploit structure to find surrogates

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C I R L Current Technical Approach Identify hard problems: –model technical problems of interest experiment to determine transition points/control variables discrete/continuous analysis of identified parameters –predict scaling behavior Apply appropriate tools to find surrogates –simple control behavior thresholds & experimental bounds on control variables –complex behavior group theory (ZAP) constraint weakening/strengthening

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C I R L Changes in Technical Approach Deëmphasized development of synthetic generators/surrogates to more quickly connect to NEST demonstration platforms. Reëmphasized computational hardness of target problems, as well as utility for NEST. Reëmphasized general modeling as opposed to search for specific surrogates.

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C I R L Progress Since Last PI Meeting Built NEST-generating system –parameterized distribution, connectivity, etc. Identified “pseudo-density” connectivity surrogate in structured NESTs –covers realistic distributions, interesting properties –identified thresholds controlling connectivity ‘Twisted tree’ disjoint spanning tree surrogate –demonstrated on various, non-idealized, distributions Discovered group-theoretic structure exploitation –potential exponential compaction of discovery process Details in technical presentation, following.

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C I R L Deliverables and Publications Generalizing Boolean Satisfiability I: Background and Existing Work. Heidi E. Dixon, Matthew L. Ginsberg, and Andrew J. Parkes: to appear in JAIR, Generalizing Boolean Satisfiability II: Theory. Heidi E. Dixon, Matthew L. Ginsberg, and Andrew J. Parkes: in preparation, to be submitted to JAIR. Generalizing Boolean Satisfiability III: Implementation. Heidi E. Dixon, Matthew L. Ginsberg, and Andrew J. Parkes: in preparation, to be submitted to JAIR. Scaling Properties of Pure Random Walk on Random 3-SAT. Andrew J. Parkes. Proceedings of the Eighth International Conference on Principles and Practice of Constraint Programming (CP2002). Published in Lecture Notes in Computer Science, LNCS Pages Easy Predictions for the Easy-Hard-Easy Transition. Andrew J. Parkes. Eighteenth Nat’l Conference on Artificial Intelligence (AAAI-02) Likely Near-Term Advances in SAT Solvers. Heidi E. Dixon, Matthew L. Ginsberg, Andrew J. Parkes, at MTV-02. Inference methods for a pseudo-Boolean satisfiability solver. Heidi E. Dixon and Matthew L. Ginsberg. AAAI-02. Six further papers are currently in preparation for submission to AAAI-03, titles will be added after the blind review period has expired.

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C I R L Success Criteria Metrics –predictive accuracy of discovered surrogates –utility of the control surrogates that are discovered –design process simplification through surrogates –generality/reusability of methodology Decision points –ability to generate predictive/control models for static problems of interest –ability to demonstrate transitions implying existence of, and to identify, surrogates for those problems

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C I R L Project Plans: Collaboration Collaborate in extreme scaling effort –help identify hard, make-or-break, issues –model problematic aspects of “ideal” approach –develop surrogates that enable minimal functionality Metric: impact of models, problems, surrogates found Assist in exploitation of existing surrogates –twisted-path implementation, etc. Metric: degree of successful exploitation Develop new surrogates –exfiltration, sentry/relay/sleep issues, scalability, etc. Metric: utility for design or modeling

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C I R L Project Plans: Modeling Study problem-distribution’s influence on surrogates –Payoff: help find useful, reliable, surrogates –Risk: open ended; difficult to determine right distributions Strengthen/weaken constraint-set to identify surrogates –Payoff: provide systematic methods –Risk: unproven; may not provide effective mechanism Off-line search (characterize search space, and identify useful gradient indicators that aid convergence) –Payoff: improved ability to find surrogates automatically –Risk: required understanding of the underlying search space may be slow in coming Metrics: in all of these, the metrics will be predictive accuracy and the ability to find useful surrogates

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C I R L Random NESTs Project Schedule and Milestones Structured NESTs Temporally structured NESTs Upcoming milestones: demonstrate use of local, static surrogates in structured NESTs discover local, static surrogates in structured NESTs determine local and global static thresholds elaborate network generator to produce more sophisticated NESTs

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C I R L Specific Milestones 1.Random NESTs/synthetic properties 1.develop parameterized network generator 2.Identify static properties of interest 3.Discover surrogates a)Identify globally observable surrogates b)Identify local surrogates 4.Determine thresholds a)for global surrogates b)for local surrogates 5.Build demonstration systems a)use global surrogates to predict behavior b)use of local surrogates Legend: On schedule Partially completed Delayed 2.Structured NESTs/synthetic properties 1.Develop network generator based on community specifications/needs 2.Identify functional properties 3.Discover surrogates a)Discover global surrogates Notes: As described previously, efforts on 1.3.b, 1.4.b, and 1.5.b were suspended in order to more quickly move the project to domains of practical interest to the NEST community. Continuing work is expected to be done to make the system developed in 2.1 more widely useful to the community.

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C I R L Technology Transition/Transfer N/A

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C I R L Program Issues N/A

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C I R L Technical Progress Summary Modeling of realistic sensor deployments –developed simulator for experiments –identified transition behavior in big-brother problem Surrogates for connectivity –pseudo-density controls many measures of interest Fairly robust routing –twisted trees: minimal disjoint spanning trees surrogate Group-theoretic structure exploitation (ZAP) –exponential simplification of certain search problems –potential for automatic generation of surrogates by simplification of generators for relevant groups

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C I R L The Overall Plan Surrogates provide computationally effective alternates to operational features that are impractical to evaluate directly

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C I R L The Overall Plan Surrogates provide computationally effective alternates to operational features that are impractical to evaluate directly Example: satisfiability in random 3-SAT –Must be possible to evaluate surrogate quickly

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C I R L The Overall Plan Surrogates provide computationally effective alternates to operational features that are impractical to evaluate directly Example: satisfiability in random 3-SAT –Must be possible to evaluate surrogate quickly –Quality/feature being modeled must have real operational use

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C I R L The Overall Plan Surrogates provide computationally effective alternates to operational features that are impractical to evaluate directly Example: satisfiability in random 3-SAT –Must be possible to evaluate surrogate quickly –Quality/feature being modeled must have real operational use –Feature being modeled must be beyond the reach of existing capabilities

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C I R L The Overall Plan Surrogates provide computationally effective alternates to operational features that are impractical to evaluate directly Example: satisfiability in random 3-SAT –Must be possible to evaluate surrogate quickly –Quality/feature being modeled must have real operational use –Feature being modeled must be beyond the reach of existing capabilities

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C I R L The Overall Plan Surrogates provide computationally effective alternates to operational features that are impractical to evaluate directly Example: satisfiability in random 3-SAT –Surrogate is clause/variable ratio –Quality/feature being modeled must have real operational use –Feature being modeled must be beyond the reach of existing capabilities

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C I R L The Overall Plan Surrogates provide computationally effective alternates to operational features that are impractical to evaluate directly Example: satisfiability in random 3-SAT –Surrogate is clause/variable ratio –Satisfiability is the coin of the realm in this domain ffff –Feature being modeled must be beyond the reach of existing capabilities

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C I R L The Overall Plan Surrogates provide computationally effective alternates to operational features that are impractical to evaluate directly Example: satisfiability in random 3-SAT –Surrogate is clause/variable ratio –Satisfiability is the coin of the realm in this domain ffff –3-SAT is NP-complete

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C I R L Multipath Routing: July Surrogates provide computationally effective alternates to operational features that are impractical to evaluate directly Example: satisfiability in random 3-SAT –Must be possible to evaluate surrogate quickly –Quality/feature being modeled must have real operational use –Feature being modeled must be beyond the reach of existing capabilities

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C I R L Multipath Routing: July Surrogates provide computationally effective alternates to operational features that are impractical to evaluate directly Example: biconnectedness –Must be possible to evaluate surrogate quickly –Quality/feature being modeled must have real operational use –Feature being modeled must be beyond the reach of existing capabilities

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C I R L Multipath Routing: July Surrogates provide computationally effective alternates to operational features that are impractical to evaluate directly Example: biconnectedness –Density as a surrogate (V 2 /N) –Quality/feature being modeled must have real operational use –Feature being modeled must be beyond the reach of existing capabilities

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C I R L Multipath Routing: July Surrogates provide computationally effective alternates to operational features that are impractical to evaluate directly Example: biconnectedness –Density as a surrogate (V 2 /N) –Quality/feature being modeled must have real operational use –Not hard! Vijay: linear-time algorithms exist

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C I R L Multipath Routing: July Surrogates provide computationally effective alternates to operational features that are impractical to evaluate directly Example: biconnectedness –Density as a surrogate (V 2 /N) –Not useful, either! –Not hard! Vijay: linear-time algorithms exist

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C I R L Multipath Routing: July Surrogates provide computationally effective alternates to operational features that are impractical to evaluate directly Example: biconnectedness –Density as a surrogate (V 2 /N) –Not useful, either! Long paths –Not hard! Vijay: linear-time algorithms exist

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C I R L Multipath Routing: July Surrogates provide computationally effective alternates to operational features that are impractical to evaluate directly Example: biconnectedness –Density as a surrogate (V 2 /N) –Not useful, either! Long paths, impossible to find –Not hard! Vijay: linear-time algorithms exist

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C I R L Multipath Routing: July Surrogates provide computationally effective alternates to operational features that are impractical to evaluate directly Example: biconnectedness –Density as a surrogate (V 2 /N) –Not useful, either! Long paths, impossible to find and who cares about disjointedness anyway? –Not hard! Vijay: linear-time algorithms exist

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C I R L Multipath Routing: December Surrogates provide computationally effective alternates to operational features that are impractical to evaluate directly Example: ability to find multiple, short, nearly disjoint routings

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C I R L Multipath Routing: December Surrogates provide computationally effective alternates to operational features that are impractical to evaluate directly Example: ability to find multiple, short, nearly disjoint routings –computationally viable surrogate

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C I R L Multipath Routing: December Surrogates provide computationally effective alternates to operational features that are impractical to evaluate directly Example: ability to find multiple, short, nearly disjoint routings –density (V 2 /N) still works

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C I R L Multipath Routing: December Surrogates provide computationally effective alternates to operational features that are impractical to evaluate directly Example: ability to find multiple, short, nearly disjoint routings –density (V 2 /N) still works –problem has to be hard

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C I R L Multipath Routing: December Surrogates provide computationally effective alternates to operational features that are impractical to evaluate directly Example: ability to find multiple, short, nearly disjoint routings –density (V 2 /N) still works –problem is known to be NP-hard (disjoint case)

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C I R L Multipath Routing: December Surrogates provide computationally effective alternates to operational features that are impractical to evaluate directly Example: ability to find multiple, short, nearly disjoint routings –density (V 2 /N) still works –problem is known to be NP-hard (disjoint case) –has to be useful

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C I R L Multipath Routing: December Surrogates provide computationally effective alternates to operational features that are impractical to evaluate directly Example: ability to find multiple, short, nearly disjoint routings –density (V 2 /N) still works –problem is known to be NP-hard (disjoint case) –clear impact on both robustness and power consumption

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C I R L Multipath Routing: December Biconnectedness is too easy Robust routing is too hard Fairly robust routing is just right And curiously enough, V 2 /N is a surrogate for all of them

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C I R L Robust Routing One way to achieve robustness is to identify multiple paths from each node to root node –other uses in load-balancing, security, … Standard algorithms are O(E+V) (Tarjan; Aho, Hopcroft, Ullman; Chang, …) –not guaranteed to return short paths –may involve many large messages Finding minimal disjoint paths is NP-hard –similarly for paths within k of optimal length –can find paths ≤ 5/3*optimal in O(E+V)

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C I R L Fairly Robust Routing Goal: “approximately disjoint” spanning trees –low cost to construct (time/communication) –short –well dispersed Approach: exploit weak localization information –augment standard flood fill with directional bias –produce a loose “spiral” in toward root Results: near-shortest-path trees –good spatial dispersion –low cost to construct –no spanning tree needed (extreme scalability)

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C I R L Twisted Trees Angular bias applied to flood fill algorithm –based on angle between arcs to neighbor and root –for a 30º left bias, choose neighbor bearing closest to 30º left of the bearing to the root Works in high surrogate density (V 2 /N) regions Serial complexity is O(V+E) –makes efficient use of distribution of sensors –conjecture: O(log(V)) parallel complexity Experimentally validated, proofs in progress –good spatial separation (not perfect!) –short paths (small multiplier of optimal)

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C I R L Gauss network graph

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C I R L Shortest path routing tree

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C I R L Boundary edges for router

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C I R L Twisted routing tree

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C I R L Multipath route

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C I R L Crop-duster network graph

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C I R L Shortest-path routing tree

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C I R L Boundary edges for router

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C I R L Twisted routing tree

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C I R L Multipath route

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C I R L A Common Surrogate Biconnectedness Robust routing Fairly robust routing V 2 /N is a surrogate for all of them

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C I R L A Common Surrogate Biconnectedness Robust routing Fairly robust routing V 2 /N is a surrogate for all of them How come?

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C I R L Continuous analysis yields order parameters: –critical clustering density: –fraction of reachable nodes: –surrogate density that controls reachability: Predicting Coverage

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C I R L Experimental Validation Connected fraction tracks prediction well

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C I R L Sensor coverage predictions

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C I R L Sensor coverage predictions

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C I R L A Common Surrogate Biconnectedness Robust routing Fairly robust routing V 2 /N is a surrogate for all of them Why?

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C I R L A Common Surrogate Biconnectedness Robust routing Fairly robust routing V 2 /N is a surrogate for all of them Because Gaussian distributions are benign

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C I R L A Common Surrogate Biconnectedness Robust routing Fairly robust routing V 2 /N is a surrogate for all of them Because Gaussian distributions are benign Suggests existence of other surrogates here:

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C I R L A Common Surrogate Biconnectedness Robust routing Fairly robust routing V 2 /N is a surrogate for all of them Because Gaussian distributions are benign Suggests existence of other surrogates here: –what is needed for exfiltration?

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C I R L A Common Surrogate Biconnectedness Robust routing Fairly robust routing V 2 /N is a surrogate for all of them Because Gaussian distributions are benign Suggests existence of other surrogates here: –what is needed for exfiltration? –how to manage sentry/relay tradeoff?

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C I R L A Common Surrogate Biconnectedness Robust routing Fairly robust routing V 2 /N is a surrogate for all of them Because Gaussian distributions are benign Suggests existence of other surrogates here: –what is needed for exfiltration? –how to manage sentry/relaysleep tradeoff? –extreme scalability: what will work?

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C I R L A Common Surrogate Biconnectedness Robust routing Fairly robust routing V 2 /N is a surrogate for all of them Because Gaussian distributions are benign Suggests existence of other surrogates here: –what is needed for exfiltration? –how to manage sentry/relay tradeoff? –extreme scalability: what will work? –surrogates avoid guesswork

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C I R L Next Steps Assist in exploitation of existing surrogates –twisted path implementation, etc. Participate in the extreme scaling effort –develop new surrogates in specific areas as needed –exfiltration, sentry/relay/sleep issues, scalability, etc. Develop tools to find surrogates in general case –as originally proposed, but harder than expected –general tools for exploiting structure (ZAP)

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