Pathfinding Algorithms for Mutating Weight Graphs

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Pathfinding Algorithms for Mutating Weight Graphs

• Haitao Mao
• Computer Systems Lab 2007-2008

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Mutating Weight Graphs

• Static graph structure
• Edge weights change over time
• Not a standard type of graph self-defined

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The Pathfinding Problem

• Given a mutating weight graph, previous states of
  the graph, a start vertex, and a destination
  vertex, find the vertex to move to next
• We are NOT finding the whole path at once
• Algorithm strength measured on cost to go from
  start to destination, complexity, and
  adaptability to different graph structures.

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Background

• Could not find any previous research on mutating
  weight graphs
• Closest field is dynamic graphs graphs which can
  gain and lose edges, but these are significantly
  different
• Other fields related to my project are
  probabilistic algorithms and graph searching
  algorithms

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A Simplification

• Grid-based graph
• All weights are 1 or infinity, and each weight
  changes between the two possibilities with
  probability p per time unit
• Destination also moves
• Actually, here the vertices are mutating, but the
  edge weights are based on the vertex weights

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Algorithms for Simplified Problem

• Dumb move randomly... eventually it'll get there
• Naive greedy algorithm with distance as
  heuristic
• Simple Dijkstra every time
• Standard take graph connectivity and structure
  into account
• Complex approximate future mutating using
  previous mutation and factor that into algorithm

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Algorithms for General Problem

• Definition randomized distance the distance to
  destination node taking graph structure into
  account. For example, a vertex with two unit
  length paths leading to the destination will be
  closer in this sense than a vertex with only one.
• Steady-state convergence/numerical analysis set
  up a system of equations we want the randomized
  distances to satisfy, and solve

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Algorithms (cont.)?

• Dynamic programming approximate distance to
  heuristically closer points first, then base
  calculations for farther vertices on these
  approximations
• Using the previous states of the graph we can
  use this data to develop a hashmap to approximate
  future mutations
• Genetic programming used to find optimal values
  for algorithm-specific variables

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Algorithm Specifications

• We focus on sparse graphs where the number of
  edges is significantly less than the square of
  the number of vertices
• Limit the edge weights to positive doubles so
  mutation will be somewhat controlled edge
  weights that are too large will never be
  traversed anyway
• Complexity should be better than
  O(E2log(E)V2log(V)) this may change

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Testing/Algorithm Analysis

• Realistically, it's hard to differentiate among
  two good algorithms
• Run all algorithms together through graphs with
  varying structure and mutation patterns compare
  based on total cost for each pathfinder, or
  possibly just their ranking
• Compare based on complexity