Adaptive Geographical Search in Networks

Andrea Wiggins

EECS 549, Winter 2007

The Problem

Geographical search in networks can be very inefficient

Need good strategies for finding the shortest (geodesic) paths

Network characteristics vary widely, and search strategies accordingly

What works for A doesn’t work for B

The Example

Example Algorithm (from Lada Adamic, SI 614, Winter 2006) current node = start node while (current node is not the target), mark current node as visited if one or more of the neighbors of the current node has not been visited,

pick the unvisited neighbor with the smallest distance to the target otherwise, pick a visited neighbor at random set the current node to the neighbor selected

In each network there are 4,000 nodes placed randomly on a two dimensional square area.

Each node is connected to its two closest neighbors (note that it may be the closest neighbor from another node's point of view, so it may gain more than two edges from this requirement).

Each node additionally adds one edge to another random node with probability 1/dr, where d is the Euclidean distance (sqrt(x2+y2)) between the two nodes, and r is the parameter that varies between the networks and takes on values 1,2, and 4.

The Results

10 trialsSteps r = 1

Steps r = 2

Stepsr = 4

Revisitsr = 1

Revisitsr = 2

Revisitsr = 4

Mean 36.6 27.2 49.4 5.1 0.9 9.7

Standard Deviation 28.0 22.9 28.6 6.2 2.2 12.4

The Proposal

Test many diverse search algorithms in parallel on a broad spectrum of network topologies with varied parameters

Adaptive agents created from elements of known successful algorithms are the search strategies being tested

Agents weight their own genes and recombine for new search algorithms

The Simulation

Environments are graphsNew but statistically similar graph for each

turn prevents local optimizationAgents’ task is to find a goal node from a

starting node in the fewest possible stepsAgents are recombined according to the

relative length of their traversals (fitness)

The Environments

Use stochastically generated graphs, on a lattice, with similar network properties

Start with Erdös-Rényi random graphs as a control - well studied standard random graphs

Study other well-known models (small worlds, etc.)

Use network growth models from the literature to create more experiments

The Agents

Agents are made up of weighted combinations of graph traversal rules

Genetic structure determines movementAgents know the relative direction of the

goal node (in 2D space)Must have memory of traversed nodes to

allow backtracking & prevent loops Usually achieved by coloring nodes

The Interactions

Condition of limited information: each node knows and can report whether it is the goal node, if it has been visited, its degree, and vector direction of its edges

Agents can ask nodes for this info, but only this info

Agents traverse the graph from a start node along the graph edges to find the goal node

The Rules

At each turn, agents traverse the graph according to their genetic instructions

At the end of the traversal, each agent adjusts its weights to credit useful strategies

After adjusting weights, agents recombine with probability based on traversal length relative to other agents

The Outcomes

Agent populations expected to converge to a few good algorithms for each graph

Rules and weights for successful algorithms will vary across graph types

Current algorithms will be discovered and surpassed

Future work can explore which search strategies work for graph characteristics

Thank you!

Questions?