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6974 results in Algorithmics, Complexity, Computer Algebra, Computational Geometry

Page 65 of 349

Complexity of Infinite-Domain Constraint Satisfaction
  • Manuel Bodirsky
  • Published online:
    28 May 2021
    Print publication:
    10 June 2021
  • Constraint Satisfaction Problems (CSPs) are natural computational problems that appear in many areas of theoretical computer science. Exploring which CSPs are solvable in polynomial time and which are NP-hard reveals a surprising link with central questions in universal algebra. This monograph presents a self-contained introduction to the universal-algebraic approach to complexity classification, treating both finite and infinite-domain CSPs. It includes the required background from logic and combinatorics, particularly model theory and Ramsey theory, and explains the recently discovered link between Ramsey theory and topological dynamics and its implications for CSPs. The book will be of interest to graduate students and researchers in theoretical computer science and to mathematicians in logic, combinatorics, and dynamics who wish to learn about the applications of their work in complexity theory.

  • The power of two choices for random walks

  • Part of
  • Agelos Georgakopoulos, John Haslegrave, Thomas Sauerwald, John Sylvester
  • Journal:
    Combinatorics, Probability and Computing / Volume 31 / Issue 1 / January 2022
    Published online by Cambridge University Press:
    28 May 2021, pp. 73-100
    • Article
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  • We apply the power-of-two-choices paradigm to a random walk on a graph: rather than moving to a uniform random neighbour at each step, a controller is allowed to choose from two independent uniform random neighbours. We prove that this allows the controller to significantly accelerate the hitting and cover times in several natural graph classes. In particular, we show that the cover time becomes linear in the number n of vertices on discrete tori and bounded degree trees, of order $${\mathcal O}(n\log \log n)$$ on bounded degree expanders, and of order $${\mathcal O}(n{(\log \log n)^2})$$ on the Erdős–Rényi random graph in a certain sparsely connected regime. We also consider the algorithmic question of computing an optimal strategy and prove a dichotomy in efficiency between computing strategies for hitting and cover times.

Page 65 of 349