scholarly journals Polynomial Time Algorithms for Variants of Graph Matching on Partial k-Trees

2016 ◽  
Vol 41 (3) ◽  
pp. 163-181
Author(s):  
Takayuki Nagoya
Keyword(s):  
Polynomial Time ◽  
Graph Matching ◽  
Graph Isomorphism ◽  
Exact Algorithms ◽  
Polynomial Time Algorithms ◽  
Np Complete

AbstractIn this paper, we deal with two variants of graph matching, the graph isomorphism with restriction and the prefix set of graph isomorphism. The former problem is known to be NP-complete, whereas the latter problem is known to be GI-complete. We propose polynomial time exact algorithms for these problems on partial k-trees.

scholarly journals Weighted Electoral Control

2015 ◽  
Vol 52 ◽  
pp. 507-542 ◽  
Author(s):  
Piotr Faliszewski ◽  
Edith Hemaspaandra ◽  
Lane A. Hemaspaandra
Keyword(s):  
Approximation Algorithms ◽  
Polynomial Time ◽  
Exact Algorithms ◽  
Weighted Voting ◽  
Np Completeness ◽  
Polynomial Time Algorithms ◽  
Np Complete ◽  
Electoral Control ◽  
Natural Settings ◽  
Work Done

Although manipulation and bribery have been extensively studied under weighted voting, there has been almost no work done on election control under weighted voting. This is unfortunate, since weighted voting appears in many important natural settings. In this paper, we study the complexity of controlling the outcome of weighted elections through adding and deleting voters. We obtain polynomial-time algorithms, NP-completeness results, and for many NP-complete cases, approximation algorithms. In particular, for scoring rules we completely characterize the complexity of weighted voter control. Our work shows that for quite a few important cases, either polynomial-time exact algorithms or polynomial-time approximation algorithms exist.

QUANTUM COMPUTATION WITH RESTRICTED AMPLITUDES

2003 ◽  
Vol 14 (05) ◽  
pp. 853-870 ◽  
Author(s):  
HARUMICHI NISHIMURA
Keyword(s):  
Quantum Computation ◽  
Polynomial Time ◽  
Exact Algorithms ◽  
Quantum Computers ◽  
Turing Machines ◽  
Computational Power ◽  
Polynomial Time Algorithms ◽  
Exact Quantum ◽  
Bounded Error ◽  
Transition Amplitudes

In this paper, we explore the power of quantum computers with restricted transition amplitudes. In 1997 Adleman, DeMarrais, and Huang showed that quantum Turing machines (QTMs) with the amplitudes from [Formula: see text] are computationally equivalent to ones with the polynomial-time computable amplitudes as machines implementing bounded-error polynomial-time algorithms. We show that QTMs with the amplitudes from [Formula: see text] is polynomial-time equivalent to deterministic Turing machines as machines implementing exact algorithms, i.e., algorithms that output correct answers with certainty. By extending this result, it is shown that exact quantum computers with rational biased coins are equivalent to classical computers. Moreover, we discuss the computational power of exact quantum computers with multiple types of coins. We also show that, from the viewpoint of zero-error polynomial-time algorithms, [Formula: see text] is not more powerful than [Formula: see text] as the set of amplitudes taken by QTMs; however, it is sufficient to solve the factoring problem.

scholarly journals Graph Isomorphism in View of Decomposition Technique

2019 ◽  
Vol 9 (2) ◽  
pp. 4773-4777
Keyword(s):  
Graph Theory ◽  
Molecular Biology ◽  
Polynomial Time ◽  
Dna Isolation ◽  
Graph Isomorphism ◽  
Decomposition Technique ◽  
Decomposition Techniques ◽  
Generic Algorithm ◽  
Polynomial Time Algorithms

Graph Isomorphism is anopen problem in graph theory. A large number of graphs have the polynomial time algorithms for detection. But in general there are specific algorithms for certain range of vertices. Our try to design a generic algorithm. In this paper we proposed an algorithm of O(n3 ) complexity. The decomposition techniques have been adopted as well as reconstruction conjecture in reverse for taking decision of whether the two graphs are isomorphic or not.The ideology is inherited from DNA isolation in molecular biology [Chomczynski et. al].

scholarly journals 3-Colorability of Pseudo-Triangulations

2015 ◽  
Vol 25 (04) ◽  
pp. 283-298
Author(s):  
Oswin Aichholzer ◽  
Franz Aurenhammer ◽  
Thomas Hackl ◽  
Clemens Huemer ◽  
Alexander Pilz ◽  
...  
Keyword(s):  
Polynomial Time ◽  
Linear Time ◽  
Plane Graphs ◽  
Np Completeness ◽  
Complete Problem ◽  
Polynomial Time Algorithms ◽  
Complexity Results ◽  
The Family ◽  
General Plane ◽  
Np Complete

Deciding 3-colorability for general plane graphs is known to be an NP-complete problem. However, for certain families of graphs, like triangulations, polynomial time algorithms exist. We consider the family of pseudo-triangulations, which are a generalization of triangulations, and prove NP-completeness for this class. This result also holds if we bound their face degree to four, or exclusively consider pointed pseudo-triangulations with maximum face degree five. In contrast to these completeness results, we show that pointed pseudo-triangulations with maximum face degree four are always 3-colorable. An according 3-coloring can be found in linear time. Some complexity results relating to the rank of pseudo-triangulations are also given.

scholarly journals Some algorithmic results for finding compatible spanning circuits in edge-colored graphs

2020 ◽  
Vol 40 (4) ◽  
pp. 1008-1019
Author(s):  
Zhiwei Guo ◽  
Hajo Broersma ◽  
Ruonan Li ◽  
Shenggui Zhang
Keyword(s):  
Polynomial Time ◽  
Sufficient Conditions ◽  
Complete Graphs ◽  
Hamilton Cycles ◽  
Colored Graph ◽  
Colored Graphs ◽  
Complete Problem ◽  
Polynomial Time Algorithms ◽  
Np Complete ◽  
Euler Tours

Abstract A compatible spanning circuit in a (not necessarily properly) edge-colored graph G is a closed trail containing all vertices of G in which any two consecutively traversed edges have distinct colors. Sufficient conditions for the existence of extremal compatible spanning circuits (i.e., compatible Hamilton cycles and Euler tours), and polynomial-time algorithms for finding compatible Euler tours have been considered in previous literature. More recently, sufficient conditions for the existence of more general compatible spanning circuits in specific edge-colored graphs have been established. In this paper, we consider the existence of (more general) compatible spanning circuits from an algorithmic perspective. We first show that determining whether an edge-colored connected graph contains a compatible spanning circuit is an NP-complete problem. Next, we describe two polynomial-time algorithms for finding compatible spanning circuits in edge-colored complete graphs. These results in some sense give partial support to a conjecture on the existence of compatible Hamilton cycles in edge-colored complete graphs due to Bollobás and Erdős from the 1970s.

EDGE-DELETION GRAPH PROBLEMS WITH FIRST-ORDER EXPRESSIBLE SUBGRAPH PROPERTIES

1991 ◽  
Vol 02 (02) ◽  
pp. 83-99
Author(s):  
V. ARVIND ◽  
S. BISWAS
Keyword(s):  
Normal Form ◽  
Polynomial Time ◽  
Edge Deletion ◽  
Present Evidence ◽  
First Order ◽  
Graph Problems ◽  
Polynomial Time Algorithms ◽  
Complete Problems ◽  
Np Complete ◽  
New Perspective

In this paper edge-deletion problems are studied with a new perspective. In general an edge-deletion problem is of the form: Given a graph G, does it have a subgraph H obtained by deleting zero or more edges such that H satisfies a polynomial-time verifiable property? This paper restricts attention to first-order expressible properties. If the property is expressed by π, which in prenex normal form is Q(Φ) where Q is the quantifier-prefix, then we prove results on the quantifier structure that characterize the complexity of the edge-deletion problem. In particular we give polynomial-time algorithms for problems for which Q is ‘simple’ and in other cases we encode certain NP-complete problems as edge-deletion problems, essentially using the quantifier structure of π. We also present evidence that Q alone cannot capture the complexity of the edge-deletion problem.

scholarly journals Hamiltonian Cycle in K1,r-Free Split Graphs — A Dichotomy

2021 ◽  
pp. 1-32
Author(s):  
P. Renjith ◽  
N. Sadagopan
Keyword(s):  
Polynomial Time ◽  
Maximum Degree ◽  
Optimization Problem ◽  
Hamiltonian Cycle ◽  
Hamiltonian Path ◽  
Np Hard ◽  
Polynomial Time Algorithms ◽  
Split Graphs ◽  
Np Complete ◽  
Cycle Path

For an optimization problem known to be NP-Hard, the dichotomy study investigates the reduction instances to determine the line separating polynomial-time solvable vs NP-Hard instances (easy vs hard instances). In this paper, we investigate the well-studied Hamiltonian cycle problem (HCYCLE), and present an interesting dichotomy result on split graphs. T. Akiyama et al. (1980) have shown that HCYCLE is NP-complete on planar bipartite graphs with maximum degree [Formula: see text]. We use this result to show that HCYCLE is NP-complete for [Formula: see text]-free split graphs. Further, we present polynomial-time algorithms for Hamiltonian cycle in [Formula: see text]-free and [Formula: see text]-free split graphs. We believe that the structural results presented in this paper can be used to show similar dichotomy result for Hamiltonian path problem and other variants of Hamiltonian cycle (path) problems.

scholarly journals POLYNOMIAL TIME ALGORITHMS FOR SOLVING NP-COMPLETE PROBLEMS

2020 ◽  
Vol 3 (441) ◽  
pp. 97-101
Author(s):  
B. Sinchev ◽  
◽  
A. B. Sinchev ◽  
Zh. Akzhanova ◽  
Y. Issekeshev ◽  
...  
Keyword(s):  
Polynomial Time ◽  
Polynomial Time Algorithms ◽  
Complete Problems ◽  
Np Complete

TERM EQUATION SATISFIABILITY OVER FINITE ALGEBRAS

2010 ◽  
Vol 20 (08) ◽  
pp. 1001-1020 ◽  
Author(s):  
TOMASZ A. GORAZD ◽  
JACEK KRZACZKOWSKI
Keyword(s):  
Computational Complexity ◽  
Polynomial Time ◽  
Finite Algebra ◽  
Satisfiability Problem ◽  
Finite Algebras ◽  
Maximal Clones ◽  
Polynomial Time Algorithms ◽  
Np Complete

We study the computational complexity of the satisfiability problem of an equation between terms over a finite algebra (TERM-SAT). We describe many classes of algebras where the complexity of TERM-SAT is determined by the clone of term operations. We classify the complexity for algebras generating maximal clones. Using this classification we describe many of algebras where TERM-SAT is NP-complete. We classify the situation for clones which are generated by an order or a permutation relation. We introduce the concept of semiaffine algebras and show polynomial-time algorithms which solve the satisfiability problem for them.

scholarly journals The Complexity of Pattern Matching for $321$-Avoiding and Skew-Merged Permutations

2016 ◽  
Vol Vol. 18 no. 2, Permutation... (Permutation Patterns) ◽  
Author(s):  
Michael H. Albert ◽  
Marie-Louise Lackner ◽  
Martin Lackner ◽  
Vincent Vatter
Keyword(s):  
Pattern Matching ◽  
Polynomial Time ◽  
Matching Problem ◽  
Polynomial Time Algorithms ◽  
Permutation Pattern ◽  
Special Cases ◽  
Np Complete

The Permutation Pattern Matching problem, asking whether a pattern permutation $\pi$ is contained in a permutation $\tau$, is known to be NP-complete. In this paper we present two polynomial time algorithms for special cases. The first algorithm is applicable if both $\pi$ and $\tau$ are $321$-avoiding; the second is applicable if $\pi$ and $\tau$ are skew-merged. Both algorithms have a runtime of $O(kn)$, where $k$ is the length of $\pi$ and $n$ the length of $\tau$.

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