New Algorithmic Paradigms in Exponential Time Algorithms

2005 ◽  
pp. 429-429
Author(s):  
Uwe Schöning
Keyword(s):  
Exponential Time ◽  
Exponential Time Algorithms

scholarly journals Application of Algorithmic Manifold to Exponential Time

2017 ◽  
Author(s):  
Takuya Yabu
Keyword(s):  
Turing Machine ◽  
Turing Machines ◽  
Topological Properties ◽  
Exponential Time ◽  
Polynomial Time Algorithms ◽  
Exponential Time Algorithms ◽  
Deterministic Turing Machine ◽  
The Relationship ◽  
Np Problem ◽  
Machine Problem

In the previous paper, I defined algorithmic manifolds simulating polynomial-time algorithms, and I showed topological properties for P problem and NP problem and that NP problem can be transformed into deterministic Turing machine problem.　In this paper, I define algorithmic manifolds simulating exponential-time algorithms and, I show topological properties for EXPTIME problem and NEXPTIME problem. I also discuss the relationship between NEXPTIME and deterministic Turing machines.

scholarly journals Deterministic single exponential time algorithms for connectivity problems parameterized by treewidth

2015 ◽  
Vol 243 ◽  
pp. 86-111 ◽  
Author(s):  
Hans L. Bodlaender ◽  
Marek Cygan ◽  
Stefan Kratsch ◽  
Jesper Nederlof
Keyword(s):  
Exponential Time ◽  
Exponential Time Algorithms ◽  
Single Exponential

scholarly journals Exact exponential-time algorithms for finding bicliques

2010 ◽  
Vol 111 (2) ◽  
pp. 64-67 ◽  
Author(s):  
Daniel Binkele-Raible ◽  
Henning Fernau ◽  
Serge Gaspers ◽  
Mathieu Liedloff
Keyword(s):  
Exponential Time ◽  
Exponential Time Algorithms

scholarly journals Faster exponential-time algorithms in graphs of bounded average degree

2015 ◽  
Vol 243 ◽  
pp. 75-85 ◽  
Author(s):  
Marek Cygan ◽  
Marcin Pilipczuk
Keyword(s):  
Average Degree ◽  
Exponential Time ◽  
Exponential Time Algorithms

Exponential time algorithms for the minimum dominating set problem on some graph classes

2009 ◽  
Vol 6 (1) ◽  
pp. 1-21 ◽  
Author(s):  
Serge Gaspers ◽  
Dieter Kratsch ◽  
Mathieu Liedloff ◽  
Ioan Todinca
Keyword(s):  
Dominating Set ◽  
Exponential Time ◽  
Minimum Dominating Set ◽  
Graph Classes ◽  
Exponential Time Algorithms ◽  
Dominating Set Problem

scholarly journals Finding and Counting Permutations via CSPs

Algorithmica ◽  
2021 ◽  
Author(s):  
Benjamin Aram Berendsohn ◽  
László Kozma ◽  
Dániel Marx
Keyword(s):  
Constraint Satisfaction ◽  
Polynomial Space ◽  
Permutation Patterns ◽  
Counting Problem ◽  
Exponential Time ◽  
Running Time ◽  
Algorithmic Question ◽  
Stack Sorting ◽  
Exponential Time Algorithms ◽  
New Algorithms

AbstractPermutation patterns and pattern avoidance have been intensively studied in combinatorics and computer science, going back at least to the seminal work of Knuth on stack-sorting (1968). Perhaps the most natural algorithmic question in this area is deciding whether a given permutation of length n contains a given pattern of length k. In this work we give two new algorithms for this well-studied problem, one whose running time is $$n^{k/4 + o(k)}$$ n k / 4 + o ( k ) , and a polynomial-space algorithm whose running time is the better of $$O(1.6181^n)$$ O ( 1 . 6181 n ) and $$O(n^{k/2 + 1})$$ O ( n k / 2 + 1 ) . These results improve the earlier best bounds of $$n^{0.47k + o(k)}$$ n 0.47 k + o ( k ) and $$O(1.79^n)$$ O ( 1 . 79 n ) due to Ahal and Rabinovich (2000) resp. Bruner and Lackner (2012) and are the fastest algorithms for the problem when $$k \in \varOmega (\log {n})$$ k ∈ Ω ( log n ) . We show that both our new algorithms and the previous exponential-time algorithms in the literature can be viewed through the unifying lens of constraint-satisfaction. Our algorithms can also count, within the same running time, the number of occurrences of a pattern. We show that this result is close to optimal: solving the counting problem in time $$f(k) \cdot n^{o(k/\log {k})}$$ f ( k ) · n o ( k / log k ) would contradict the exponential-time hypothesis (ETH). For some special classes of patterns we obtain improved running times. We further prove that 3-increasing (4321-avoiding) and 3-decreasing (1234-avoiding) permutations can, in some sense, embed arbitrary permutations of almost linear length, which indicates that a sub-exponential running time is unlikely with the current techniques, even for patterns from these restricted classes.

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