Skip to main content Accessibility help
×
  1. Home
  2. Browse subjects
  3. Computer Science
  4. Algorithmics, Complexity, Computer Algebra, Computational Geometry
  5. Content listing

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

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

Page 70 of 349

  • Near-perfect clique-factors in sparse pseudorandom graphs

  • Part of
  • Jie Han, Yoshiharu Kohayakawa, Yury Person
  • Journal:
    Combinatorics, Probability and Computing / Volume 30 / Issue 4 / July 2021
    Published online by Cambridge University Press:
    11 December 2020, pp. 570-590

  • We prove that, for any $t \ge 3$, there exists a constant c = c(t) > 0 such that any d-regular n-vertex graph with the second largest eigenvalue in absolute value λ satisfying $\lambda \le c{d^{t - 1}}/{n^{t - 2}}$ contains vertex-disjoint copies of kt covering all but at most ${n^{1 - 1/(8{t^4})}}$ vertices. This provides further support for the conjecture of Krivelevich, Sudakov and Szábo (Combinatorica 24 (2004), pp. 403–426) that (n, d, λ)-graphs with n ∈ 3ℕ and $\lambda \le c{d^2}/n$ for a suitably small absolute constant c > 0 contain triangle-factors. Our arguments combine tools from linear programming with probabilistic techniques, and apply them in a certain weighted setting. We expect this method will be applicable to other problems in the field.

Competitive Programming in Python
  • 128 Algorithms to Develop your Coding Skills
  • Christoph Dürr, Jill-Jênn Vie
  • Translated by Greg Gibbons, Danièle Gibbons
  • Published online:
    03 December 2020
    Print publication:
    17 December 2020
  • Want to kill it at your job interview in the tech industry? Want to win that coding competition? Learn all the algorithmic techniques and programming skills you need from two experienced coaches, problem setters, and jurors for coding competitions. The authors highlight the versatility of each algorithm by considering a variety of problems and show how to implement algorithms in simple and efficient code. Readers can expect to master 128 algorithms in Python and discover the right way to tackle a problem and quickly implement a solution of low complexity. Classic problems like Dijkstra's shortest path algorithm and Knuth-Morris-Pratt's string matching algorithm are featured alongside lesser known data structures like Fenwick trees and Knuth's dancing links. The book provides a framework to tackle algorithmic problem solving, including: Definition, Complexity, Applications, Algorithm, Key Information, Implementation, Variants, In Practice, and Problems. Python code included in the book and on the companion website.

  • Large complete minors in random subgraphs

  • Part of
  • Joshua Erde, Mihyun Kang, Michael Krivelevich
  • Journal:
    Combinatorics, Probability and Computing / Volume 30 / Issue 4 / July 2021
    Published online by Cambridge University Press:
    03 December 2020, pp. 619-630

  • Let G be a graph of minimum degree at least k and let Gp be the random subgraph of G obtained by keeping each edge independently with probability p. We are interested in the size of the largest complete minor that Gp contains when p = (1 + ε)/k with ε > 0. We show that with high probability Gp contains a complete minor of order $\tilde{\Omega}(\sqrt{k})$, where the ~ hides a polylogarithmic factor. Furthermore, in the case where the order of G is also bounded above by a constant multiple of k, we show that this polylogarithmic term can be removed, giving a tight bound.

  • Generalizations of the Ruzsa–Szemerédi and rainbow Turán problems for cliques

  • Part of
  • W. T. Gowers, Barnabás Janzer
  • Journal:
    Combinatorics, Probability and Computing / Volume 30 / Issue 4 / July 2021
    Published online by Cambridge University Press:
    19 November 2020, pp. 591-608
    • Article
      • You have access
      • Open access
    • PDF
    • Export citation

  • Considering a natural generalization of the Ruzsa–Szemerédi problem, we prove that for any fixed positive integers r, s with r < s, there are graphs on n vertices containing $n^{r}e^{-O\left(\sqrt{\log{n}}\right)}=n^{r-o(1)}$ copies of Ks such that any Kr is contained in at most one Ks. We also give bounds for the generalized rainbow Turán problem ex (n, H, rainbow - F) when F is complete. In particular, we answer a question of Gerbner, Mészáros, Methuku and Palmer, showing that there are properly edge-coloured graphs on n vertices with $n^{r-1-o(1)}$ copies of Kr such that no Kr is rainbow.

Page 70 of 349