scholarly journals HybridHAM: A Novel Hybrid Heuristic for Finding Hamiltonian Cycle

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
K. R. Seeja
Keyword(s):  
Hamiltonian Cycle ◽  
Hamiltonian Path ◽  
Exact Algorithms ◽  
Combinatorial Problems ◽  
Second Phase ◽  
Worst Case ◽  
Hybrid Heuristic ◽  
Depth First Search ◽  
Initial Path ◽  
Rotational Transformation

Hamiltonian Cycle Problem is one of the most explored combinatorial problems. Being an NP-complete problem, heuristic approaches are found to be more powerful than exponential time exact algorithms. This paper presents an efficient hybrid heuristic that sits in between the complex reliable approaches and simple faster approaches. The proposed algorithm is a combination of greedy, rotational transformation and unreachable vertex heuristics that works in three phases. In the first phase, an initial path is created by using greedy depth first search. This initial path is then extended to a Hamiltonian path in second phase by using rotational transformation and greedy depth first search. Third phase converts the Hamiltonian path into a Hamiltonian cycle by using rotational transformation. The proposed approach could find Hamiltonian cycles from a set of hard graphs collected from the literature, all the Hamiltonian instances (1000 to 5000 vertices) given in TSPLIB, and some instances of FHCP Challenge Set. Moreover, the algorithm has O(n3) worst case time complexity. The performance of the algorithm has been compared with the state-of-the-art algorithms and it was found that HybridHAM outperforms others in terms of running time.

A Parallel Reduction of Hamiltonian Cycle to Hamiltonian Path in Tournaments

1995 ◽  
Vol 19 (3) ◽  
pp. 432-440 ◽  
Author(s):  
E. Bampis ◽  
M. Elhaddad ◽  
Y. Manoussakis ◽  
M. Santha
Keyword(s):  
Hamiltonian Cycle ◽  
Hamiltonian Path ◽  
Parallel Reduction

Memory-Aware Scheduling Parallel Real-Time Tasks for Multicore Systems

2021 ◽  
Vol 31 (04) ◽  
pp. 613-634
Author(s):  
Zhenyang Lei ◽  
Xiangdong Lei ◽  
Jun Long
Keyword(s):  
Real Time ◽  
Data Access ◽  
Main Memory ◽  
Second Phase ◽  
Shared Resources ◽  
Access Memory ◽  
Worst Case ◽  
Scheduling Policy ◽  
The Core ◽  
Level Scheduling

Shared resources on the multicore chip, such as main memory, are increasingly becoming a point of contention. Traditional real-time task scheduling policies focus on solely on the CPU, and do not take in account memory access and cache effects. In this paper, we propose parallel real-time tasks scheduling (PRTTS) policy on multicore platforms. Each set of tasks is represented as a directed acyclic graph (DAG). The priorities of tasks are assigned according to task periods Rate Monotonic (RM). Each task is composed of three phases. The first phase is read memory stage, the second phase is execution phase and the third phase is write memory phase. The tasks use locks and critical sections to protect data access. The global scheduler maintains the task pool in which tasks are ready to be executed which can run on any core. PRTTS scheduling policy consists of two levels: the first level scheduling schedules ready real-time tasks in the task pool to cores, and the second level scheduling schedules real-time tasks on cores. Tasks can preempt the core on running tasks of low priority. The priorities of tasks which want to access memory are dynamically increased above all tasks that do not access memory. When the data accessed by a task is in the cache, the priority of the task is raised to the highest priority, and the task is scheduled immediately to preempt the core on running the task not accessing memory. After accessing memory, the priority of these tasks is restored to the original priority and these tasks are pended, the preempted task continues to run on the core. This paper analyzes the schedulability of PRTTS scheduling policy. We derive an upper-bound on the worst-case response-time for parallel real-time tasks. A series of extensive simulation experiments have been performed to evaluate the performance of proposed PRTTS scheduling policy. The results of simulation experiment show that PRTTS scheduling policy offers better performance in terms of core utilization and schedulability rate of tasks.

Worst-case Complexity of Exact Algorithms forNP-hard Problems

2010 ◽  
pp. 203-240
Author(s):  
Federico Della Croce ◽  
Bruno Escoffier ◽  
Marcin Kamiski ◽  
Vangelis Th. Paschos
Keyword(s):  
Exact Algorithms ◽  
Worst Case ◽  
Case Complexity ◽  
Worst Case Complexity ◽  
Hard Problems

NONLINEAR COMPUTABILITY BASED ON CHAOS

2000 ◽  
Vol 10 (02) ◽  
pp. 415-429 ◽  
Author(s):  
GABRIELE MANGANARO ◽  
JOSE PINEDA DE GYVEZ
Keyword(s):  
Hamiltonian Path ◽  
Combinatorial Problem ◽  
Combinatorial Problems ◽  
Information Coding ◽  
Computing Power ◽  
Complete Problems ◽  
Np Complete ◽  
Systematic Solution ◽  
Chaotic Simulated Annealing ◽  
Computing Models

Two new computing models based on information coding and chaotic dynamical systems are presented. The novelty of these models lies on the blending of chaos theory and information coding to solve complex combinatorial problems. A unique feature of our computing models is that despite the nonpredictability property of chaos, it is possible to solve any combinatorial problem in a systematic way, and with only one dynamical system. This is in sharp contrast to methods based on heuristics employing an array of chaotic cells. To prove the computing power and versatility of our models, we address the systematic solution of classical NP-complete problems such as the three colorability and the directed Hamiltonian path in addition to a new chaotic simulated annealing scheme.

scholarly journals Dynastic Potential Crossover Operator

2021 ◽  
pp. 1-35
Author(s):  
Francisco Chicano ◽  
Gabriela Ochoa ◽  
L. Darrell Whitley ◽  
Renato Tinós
Keyword(s):  
Polynomial Time ◽  
Population Based ◽  
Combinatorial Problems ◽  
Crossover Operator ◽  
Empirical Comparison ◽  
Worst Case ◽  
Optimal Recombination ◽  
Max Sat ◽  
Variable Interaction

Abstract An optimal recombination operator for two parent solutions provides the best solution among those that take the value for each variable from one of the parents (gene transmission property). If the solutions are bit strings, the offspring of an optimal recombination operator is optimal in the smallest hyperplane containing the two parent solutions. Exploring this hyperplane is computationally costly, in general, requiring exponential time in the worst case. However, when the variable interaction graph of the objective function is sparse, exploration can be done in polynomial time. In this paper, we present a recombination operator, called Dynastic Potential Crossover (DPX), that runs in polynomial time and behaves like an optimal recombination operator for low-epistasis combinatorial problems. We compare this operator, both theoretically and experimentally, with traditional crossover operators, like uniform crossover and network crossover, and with two recently defined efficient recombination operators: partition crossover and articulation points partition crossover. The empirical comparison uses NKQ Landscapes and MAX-SAT instances. DPX outperforms the other crossover operators in terms of quality of the offspring and provides better results included in a trajectory and a population-based metaheuristic, but it requires more time and memory to compute the offspring.

scholarly journals Hypothetical Accident in Polish Nuclear Power Plant. Worst Case Scenario for Main Polish Cities

2019 ◽  
Vol 26 (1) ◽  
pp. 9-28
Author(s):  
Andrzej Mazur
Keyword(s):  
Power Plant ◽  
Nuclear Power Plant ◽  
Nuclear Power ◽  
Power Plants ◽  
Atmospheric Transport ◽  
Radioactive Material ◽  
Second Phase ◽  
Pollution Transport ◽  
Worst Case ◽  
Hypothetical Accident

Abstract Poland is under threat of potential accidents in nuclear power plants located in its close vicinity, in almost all neighboring countries. Moreover, there are plans to establish a new nuclear power plant in Polish coast. In this paper the analysis of atmospheric transport of radioactive material released during a potential accident in the future nuclear power plant is presented. In the first part of study transport of radioactivity as seen from the long time perspective is analyzed. This involves trajectory analysis as a tool for describing the statistics of air pollution transport pattern and screening the meteorological situations for episode studies. Large sets of meteorological data for selected episodes were stored as a result of this process. Estimation of risk includes both analysis of the consequences and probability analysis of an occurrence of such situation. Episodes then were comprehensively studied in the second phase of the study, using the Eulerian dispersion model for simulation of atmospheric transport of pollutants. This study has proven that the time needed for reaction in case of (hypothetical) accident is enormously short.

scholarly journals An Effective Algorithm for and Phase Transitions of the Directed Hamiltonian Cycle Problem

2010 ◽  
Vol 39 ◽  
pp. 663-687 ◽  
Author(s):  
G. Jäger ◽  
W. Zhang
Keyword(s):  
Phase Transitions ◽  
Hamiltonian Cycle ◽  
Directed Graphs ◽  
Combinatorial Problem ◽  
Combinatorial Problems ◽  
Effective Algorithm ◽  
Intrinsic Properties ◽  
Award Winning ◽  
Close Relationship ◽  
Hamiltonian Cycle Problem

The Hamiltonian cycle problem (HCP) is an important combinatorial problem with applications in many areas. It is among the first problems used for studying intrinsic properties, including phase transitions, of combinatorial problems. While thorough theoretical and experimental analyses have been made on the HCP in undirected graphs, a limited amount of work has been done for the HCP in directed graphs (DHCP). The main contribution of this work is an effective algorithm for the DHCP. Our algorithm explores and exploits the close relationship between the DHCP and the Assignment Problem (AP) and utilizes a technique based on Boolean satisfiability (SAT). By combining effective algorithms for the AP and SAT, our algorithm significantly outperforms previous exact DHCP algorithms, including an algorithm based on the award-winning Concorde TSP algorithm. The second result of the current study is an experimental analysis of phase transitions of the DHCP, verifying and refining a known phase transition of the DHCP.

scholarly journals Space-Efficient Fully Dynamic DFS in Undirected Graphs †

Algorithms ◽  
2019 ◽  
Vol 12 (3) ◽  
pp. 52 ◽  
Author(s):  
Kengo Nakamura ◽  
Kunihiko Sadakane
Keyword(s):  
Undirected Graph ◽  
Undirected Graphs ◽  
Edge Connectivity ◽  
Worst Case ◽  
Depth First Search ◽  
Insertions And Deletions ◽  
Adjacency List ◽  
Graph Traversal ◽  
Dynamic Connectivity ◽  
Traversal Algorithm

Depth-first search (DFS) is a well-known graph traversal algorithm and can be performed in O ( n + m ) time for a graph with n vertices and m edges. We consider the dynamic DFS problem, that is, to maintain a DFS tree of an undirected graph G under the condition that edges and vertices are gradually inserted into or deleted from G. We present an algorithm for this problem, which takes worst-case O ( m n · polylog ( n ) ) time per update and requires only ( 3 m + o ( m ) ) log n bits of space. This algorithm reduces the space usage of dynamic DFS algorithm to only 1.5 times as much space as that of the adjacency list of the graph. We also show applications of our dynamic DFS algorithm to dynamic connectivity, biconnectivity, and 2-edge-connectivity problems under vertex insertions and deletions.

scholarly journals Maximum graphs non-Hamiltonian-connected from a vertex

1984 ◽  
Vol 25 (1) ◽  
pp. 97-98
Author(s):  
G. R. T. Hendry
Keyword(s):  
Hamiltonian Cycle ◽  
Hamiltonian Path ◽  
Hamiltonian Graphs ◽  
Connected Graphs ◽  
Hamiltonian Connected

A path (cycle) in a graph G is called a hamiltonian path (cycle) of G if it contains every vertex of G. A graph is hamiltonian if it contains a hamiltonian cycle. A graph G is hamiltonian-connectedif it contains a u-vhamiltonian path for each pair u, v of distinct vertices of G. A graph G is hamiltonian-connected from a vertex v of G if G contains a v-whamiltonian path for each vertex w≠v. Considering only graphs of order at least 3, the class of graphs hamiltonian-connected from a vertex properly contains the class of hamiltonian-connected graphs and is properly contained in the class of hamiltonian graphs.

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