• Corpus ID: 6482756

The Branching Factor of Regular Search Spaces

@inproceedings{Edelkamp1998TheBF,
  title={The Branching Factor of Regular Search Spaces},
  author={Stefan Edelkamp and Richard E. Korf},
  booktitle={AAAI/IAAI},
  year={1998}
}
Many problems, such as the sliding-tile puzzles, generate search trees where different nodes have different numbers of children, in this case depending on the position of the blank. We show how to calculate the asymptotic branching factors of such problems, and how to efficiently compute the exact numbers of nodes at a given depth. This information is important for determining the complexity of various search algorithms on these problems. In addition to the slidingg-tile puzzles, we also apply… 

Figures from this paper

Recent Progress in the Design and Analysis of Admissible Heuristic Functions

  • R. Korf
  • Computer Science
    AAAI/IAAI
  • 2000
This work has learned how to accurately predict the running time of admissible heuristic search algorithms, as a function of the solution depth and the heuristic evaluation function.

Complexity Analysis of Admissible Heuristic Search

The asymptotic time complexity of admissible heuristic search algorithms such as A*, IDA*, and depth-first branch-and-bound is analyzed to accurately predict the performance of these algorithms on problems such as the slidingtile puzzles and Rubik's Cube.

Time complexity of iterative-deepening-A*

A Topological Approach to Meta-heuristics: Analytical Results on the BFS vs. DFS Algorithm Selection Problem

Estimates for average BFS and DFS runtime are derived using a probabilistic model of goal distribution and an additional statistic of path redundancy and average branching factor for tree search and graph search.

Finding Optimal Solutions to Atomix

Backward search is shown to be viable, since the branching factor can be proven to be the same as for forward search in the heuristic algorithm A*.

Enhanced Partial Expansion A

A novel variant of A* called Enhanced Partial Expansion A* (EPEA*) is presented that advances the idea of PEA* to address the time aspect and shows significant improvements in run-time and memory performance for several standard benchmark applications.

How to Solve the Traveling Salesman Problem

The Traveling Salesman Problem (TSP) is believed to be an intractable problem and have no practically efficient algorithm to solve it. The intrinsic difficulty of the TSP is associated with the

Solving Random Satisfiability Problems with Quantum Computers

An approximate asymptotic analysis accounting for both the average and variation of amplitudes among search states with the same costs predicts good performance, on average, for a variety of problems including those near a phase transition associated with a high concentration of hard cases.

A new approach to the traveling salesman problem

  • Weiqi Li
  • Computer Science
    ACM Southeast Regional Conference
  • 2022
A new search strategy for solving the Traveling Salesman Problem is described that combines local search and exhausted search and is treated as a discrete dynamical system.

A New Challenge: Approaching Tetris Link with AI

This paper introduces a board game, Tetris Link, that is yet unexplored and appears to be highly challenging, and explores heuristic planning and two other approaches: Reinforcement Learning and Monte Carlo tree search.

References

SHOWING 1-10 OF 10 REFERENCES

Pruning Duplicate Nodes in Depth-First Search

This work presents a technique for reducing the asymptotic complexity of depth-first search by eliminating the generation of duplicate nodes, and implements and tests the technique on a grid, the Fifteen Puzzle, the Twenty-Four Puzzle, and two versions of Rubik's Cube.

Depth-First Iterative-Deepening: An Optimal Admissible Tree Search

  • R. Korf
  • Computer Science
    Artif. Intell.
  • 1985

Suux Tree Automata in State Space Search

An on{line learning algorithm for pruning state space search is described in this paper based on a nite state machine which is both created and used in the search.

Suffix Tree Automata in State Space Search

An on-line learning algorithm for pruning state space search is described in this paper based on a finite state machine which is both created and used in the search.

Randomized Algorithms

These notes describe other important illustrations of randomized algo rithms in other areas of the theory of algorithms and describe some basic principles which typically underly the construction of randomized algorithms.

Su x tree automata in state

  • 1997

Depth-first iterative-deepening: an optimal admissible tree search

Markov Chains

Depth- rst iterative-deepening

  • 1985

Figure 6: An automaton for predecessor elimination in the sliding tile puzzle

  • Figure 6: An automaton for predecessor elimination in the sliding tile puzzle