Formal Complexity Analysis of RoboFlag Drill & Communication and Computation in Distributed Negotiation Algorithms Carla P. Gomes Cornell University. Formal Complexity Analysis of RoboFlag Drill. (joint work with Matt Earl and Raff D’Andrea). Question:
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Formal Complexity Analysis of RoboFlag Drill
&
Communication and Computation
in Distributed Negotiation Algorithms
Carla P. Gomes
Cornell University
Formal Complexity Analysis of RoboFlag Drill
(joint work with Matt Earl and Raff D’Andrea)
Question:
What is the computational complexity
of Roboflag Drill?
Find the simplest particular case of Roboflag Drill for which we can formally prove that the task is NP-complete – Roboflag Drill Base
– Find a known NP-complete problem, Q
– Reduce Q to Roboflag Drill Base,
using a polynomial time reduction
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?
NP-Complete Problem Q:
TDET - Scheduling tasks with time depend execution times
Input:
Set of tasks
release time
deadline
processing time – dependent on start time;
One processor
Question: Can we schedule all the task on the single processor, so that they are all processed before the deadlines?
NP-complete in the strong sense
Attackers all equidistant from the goal area:
Polynomial
(becomes NP-Complete with only two different distances)
Fixed number of attackers:
Fixed Parameter Complexity Class
Communication and Computation
in Distributed Negotiation Algorithms
(joint work with Cesar Fernandez, Bhaskar Krishnamachari, and Bart Selman)
A4
m1
m2
m3
A1
A2
A3
The behaviour of Distributed Negotiation algorithms
DN algorithms solve a problem through a distributed computational search process
Agents exchange messages for reaching a global solution
The arrival order of the messages determines the decisions of A4
Distributed Negotiation Problems (DNP)
Pi belongs to Ai: only Ai can modify the variables of Pi
SensorDNP - a benchmark problem
DNP algorithms
We consider only complete algorithms: they always find a solution if there exists one
ABT: Static priority order.
AWC: Dynamic priority order and min-conflict heuristic.
DNP algorithms - randomization and restarting
Modifications to the DNP algorithms:
Network traffic models and delay distributions
Exponential delay distributions
Log-normal and Fractional Gaussian Noise
delay distributions
Our results: delays introduced by the network can improve the performance of DNP algorithms
Exponential delay links: results
exponentially distributed delays
Pc : Compatibility level between sensors (0 to 1)
Pv : Visibility level of sensors (0 to 1)
PC and PV model the level of resources available
Phase Transition in SensorDNP
Sharp transition to solvable instances at critical level of resources
Mean complexity
Peak in complexity around phase transition region
Worse for low level of compatibility (Pc)
Psat = 0.2
Psat = 0.8
Active delaying of messages
Results on a hard soluble instance
Comparing different delay distributions
Performance is improved when using restarting
Cost distributions when solving a hard soluble instance
using restarting
Summary
Studying reduction from TDET
(Tasks with Time Dependent Execution Times)
Phase transition phenomena with corresponding peak in complexity for distributed negotiation protocols;
Controlled randomization can increase performance of negotiation protocols dramatically.