Transcript Power point presentation.

Formal Complexity Analysis of
Mobile Problems
&
Communication and Computation
in Distributed Sensor Networks
Carla P. Gomes
Cornell University
Formal Complexity Analysis of Mobile Problems
(joint work with Matt Earl and Raff D’Andrea)
Target Assignment Problem
Input:
Set of attackers
initial location
velocity
direction
One or more defenders
initial location
velocity
direction
Question: Can the defenders intersect all the attackers
in a given time?
Formal Complexity Analysis of Target Assignment
Problem
Question:
What is the computational complexity
of Target Assignment problem?
Formal Complexity Analysis of Target Assignment
Problem
- NP-hard problem
Reduction from Euclidean TSP
Formal Complexity Analysis of Target Assignment
Problem
Approximations
This problem is approximable within a
constant factor of the optimal solution, in
polynomial time;
it admits a PTAS (polynomial time
approximation scheme that allows us to
be arbitrarily close to the optimum;
polynomial in the length of the input but
not polynomial in the performance ratio)
RoboFlag Drill Base
Input:
Set of attackers
initial location
velocity (constant)
direction (constant)
One defender
initial location
velocity (constant)
direction – piecewise linear
Goal area
Question: Can the defender intersect all the attackers
before they reach the goal area?
Formal Complexity Analysis of Roboflag Drill
Problem
Question:
What is the computational complexity
of Roboflag Drill?
RoboFlag Drill Base
(conjectures)
NP-hard for the general problem
Polynomial for some classes (e.g., if the attackers
move in parallel and if they are equidistant from
the goal area)
Fixed number of attackers:
Fixed Parameter Complexity Class
Communication and Computation
in Distributed Sensor Networks
(joint work with Carmel Domshlak and Bart
Selman)
Communication and Computation in
Distributed Negotiation Algorithms
Carla Gomes, Bart
Selman,
Carmel Domshlak
IISI - Cornell
Sensor Network Problem
Sensors { s1 , …, sn }.
Targets { 1 , …, m }.
Given a spatial model of the problem domain, and
the locations of the targets, determine whether there
exists a set of m sensor triplets such that:
1.
Sensors within each triplet can
communicate one with each other.
2.
All three sensors in the i –th triplet can
track the target i .
3.
All the triplets are pairwise sensor-disjoint.
From a general model to real-life settings
Spatial Modeling
 Sensor model
 Possible locations on the terrain.
 Communication model
 Communication abilities of the sensors as a function
of basic sensor spec and the terrain conditions.
 Visibility model
 Tracking abilities of the sensors as a function of target
parameters, basic sensor spec and the terrain
conditions.
From a general model to real-life settings
Spatial Modeling
• Sensor model
– Possible locations on the terrain.
•
Communication model
– Communication abilities of the sensors as a function
of basic sensor spec and the terrain conditions.
•
Visibility model
– Tracking abilities of the sensors as a function of target
parameters, basic sensor spec and the terrain
conditions.
Complexity analysis of computation and communication
of negotiation protocols on problems modelled as
above.
– Formal analysis
– Empirical analysis
P
NP-hard
From a general model to real-life settings
Spatial Modeling
• Sensor model
– Possible locations on the terrain.
•
Communication model
– Communication abilities of the sensors as a function
of basic sensor spec and the terrain conditions.
•
Visibility model
– Tracking abilities of the sensors as a function of target
parameters, basic sensor spec and the terrain
conditions.
Complexity analysis of computation and communication
of negotiation protocols on problems modelled as
above.
– Formal analysis
– Empirical analysis
Temporal model of moving targets
– Analysis of alternative (complete) renegotiation
schemes.
– Can we renegotiate in real-life settings?
P
NP-hard
Results
Spatial Modeling
A Grid-based sensor network model has been developed.
•
•
The locality of sensor communicability and target visibility is
modeled via controlled parameters.
The constraintness of communicability and visibility is
modeled via probability distributions w.r.t. the locality
parameters.
pv
kv
N
pc
m
Order of
the
problem
kc
Level of
decomposition
(locality)
Level of
constraintness
Results
Spatial Modeling
A Grid-based sensor network model developed.
•
•
The locality of sensor communicability and target visibility is
modeled via controlled parameters.
The constrainedness of communicability and visibility is
modeled via probability distributions w.r.t. the locality
parameters.
Complexity analysis of computation and communication of
negotiation protocols.
•
•
Formal analysis covering all the subclasses of the problem
– Identified polynomial algorithms for tractable cases (e.g.,
(1) when visibility is restricted to small window and (2)
communication is locally complete (local graph is
complete)).
– Non-trivial NP-completeness proofs for intractable cases.
Comprehensive empirical analysis.
pv
kv
N
pc
m
Order of
the
problem
kc
Level of
decomposition
(locality)
Level of
constraintness
Results
Spatial Modeling
A Grid-based sensor network model has been developed.
•
•
The locality of sensor communicability and target visibility is
modeled via controlled parameters.
The constrainedness of communicability and visibility is
modeled via probability distributions w.r.t. the locality
parameters.
Complexity analysis of computation and communication of
negotiation protocols.
•
•
Formal analysis covering all the subclasses of the problem
– Polynomial algorithms for tractable cases
– Non-trivial NP-completeness proofs for intractable cases.
Comprehensive empirical analysis.
Temporal model of moving targets
•
•
Several algorithms for dynamic renegotiation have been
analysed in the scope of a specially designed evaluation
framework.
Complete renegotiation has been shown to be practically
feasible.
pv
kv
N
pc
Level of
constraintness
m
Order of
the
problem
kc
Level of
decomposition
(locality)
Mean time to solve:
Renegotiation – 0.059 sec
Negotiation from scratch –
0.084 sec
Phase Transition in SensorDNP
Sharp transition in solvability at critical level of resources
(Pc – probability of communication; Pv – probability of
visibility)
Summary
 Formal Complexity Analysis of Mobile Problems
 Distributed Sensor Networks
Complexity analysis
Phase transition phenomena with corresponding peak in
complexity for distributed sensor networks;
Controlled randomization can increase performance of
negotiation protocols dramatically.