Dealing with Hardness

2017 ◽  
Author(s):  
Lance Fortnow
Keyword(s):  
Brute Force ◽  
Complete Problem ◽  
Hard Problems ◽  
Np Complete ◽  
Np Problems ◽  
Single Technique

This chapter demonstrates several approaches for dealing with hard problems. These approaches include brute force, heuristics, and approximation. Typically, no single technique will suffice to handle the difficult NP problems one needs to solve. For moderate-sized problems one can search over all possible solutions with the very fast computers available today. One can use algorithms that might not work for every problem but do work for many of the problems one cares about. Other algorithms may not find the best possible solution but still a solution that's good enough. Other times one just cannot get a solution for an NP-complete problem. One has to try to solve a different problem or just give up.

NP vs QMA_\log(2)

2010 ◽  
Vol 10 (1&2) ◽  
pp. 141-151
Author(s):  
S. Beigi
Keyword(s):  
Quantum Algorithms ◽  
Np Hard ◽  
Complete Problems ◽  
Hard Problems ◽  
Np Complete ◽  
Np Hard Problems

Although it is believed unlikely that $\NP$-hard problems admit efficient quantum algorithms, it has been shown that a quantum verifier can solve NP-complete problems given a "short" quantum proof; more precisely, NP\subseteq QMA_{\log}(2) where QMA_{\log}(2) denotes the class of quantum Merlin-Arthur games in which there are two unentangled provers who send two logarithmic size quantum witnesses to the verifier. The inclusion NP\subseteq QMA_{\log}(2) has been proved by Blier and Tapp by stating a quantum Merlin-Arthur protocol for 3-coloring with perfect completeness and gap 1/24n^6. Moreover, Aaronson et al. have shown the above inclusion with a constant gap by considering $\widetilde{O}(\sqrt{n})$ witnesses of logarithmic size. However, we still do not know if QMA_{\log}(2) with a constant gap contains NP. In this paper, we show that 3-SAT admits a QMA_{\log}(2) protocol with the gap 1/n^{3+\epsilon}} for every constant \epsilon>0.

A Novel Bio Inspired Algorithm Based on Echolocation Mechanism of Bats for Seismic States Prediction

2017 ◽  
Vol 8 (3) ◽  
pp. 1-18 ◽  
Author(s):  
Mohamed Elhadi Rahmani ◽  
Abdelmalek Amine ◽  
Reda Mohamed Hamou
Keyword(s):  
Data Mining ◽  
Seismic Hazard ◽  
Ground Motion ◽  
Geographic Area ◽  
Seismic Hazards ◽  
Data Discovery ◽  
Distance Calculation ◽  
Hard Problems ◽  
Recorded Data ◽  
Np Problems

Bio-inspired algorithms are sort of implementation of natural solutions to solve hard problems – so called NP problems. A seismic hazard is the probability that an earthquake will occur in a given geographic area, within a given window of time, and with ground motion intensity exceeding a given threshold. Seismic hazards prediction is one of the fields where data mining plays an important role. This paper presents a new bio-inspired algorithm motivated by the echolocation behavior of bats for seismic hazard states prediction in coal mines based on previously recorded data. It is a distance calculation based approach, Results were very satisfactory in a manner that encourage us to continue working on this approach. The implementation of the algorithm touches three fields of studies, data discovery or so called data mining, bio inspired techniques, and seismic hazards predictions.

scholarly journals Statistical mechanics of an NP-complete problem: subset sum

2001 ◽  
Vol 34 (44) ◽  
pp. 9555-9567 ◽  
Author(s):  
Tomohiro Sasamoto ◽  
Taro Toyoizumi ◽  
Hidetoshi Nishimori
Keyword(s):  
Statistical Mechanics ◽  
Complete Problem ◽  
Subset Sum ◽  
Np Complete

scholarly journals Consecutive Colouring of Oriented Graphs

2021 ◽  
Vol 76 (4) ◽  
Author(s):  
Marta Borowiecka-Olszewska ◽  
Ewa Drgas-Burchardt ◽  
Nahid Yelene Javier-Nol ◽  
Rita Zuazua
Keyword(s):  
Planar Graphs ◽  
Maximum Degree ◽  
Bipartite Graphs ◽  
Complete Graphs ◽  
Oriented Graphs ◽  
Complete Problem ◽  
Np Complete

AbstractWe consider arc colourings of oriented graphs such that for each vertex the colours of all out-arcs incident with the vertex and the colours of all in-arcs incident with the vertex form intervals. We prove that the existence of such a colouring is an NP-complete problem. We give the solution of the problem for r-regular oriented graphs, transitive tournaments, oriented graphs with small maximum degree, oriented graphs with small order and some other classes of oriented graphs. We state the conjecture that for each graph there exists a consecutive colourable orientation and confirm the conjecture for complete graphs, 2-degenerate graphs, planar graphs with girth at least 8, and bipartite graphs with arboricity at most two that include all planar bipartite graphs. Additionally, we prove that the conjecture is true for all perfect consecutively colourable graphs and for all forbidden graphs for the class of perfect consecutively colourable graphs.

Quality of Service for Multimedia and Real-Time Services

2010 ◽  
Vol 5 (4) ◽  
pp. 1-22
Author(s):  
F. W. Albalas ◽  
B. A. Abu-Alhaija ◽  
A. Awajan ◽  
A. Awajan ◽  
Khalid Al-Begain
Keyword(s):  
Decision Making ◽  
Quality Of Service ◽  
Real Time ◽  
Qos Routing ◽  
Routing Algorithms ◽  
Complete Problem ◽  
Filtering Technique ◽  
Np Complete ◽  
Multiple Metrics

New web technologies have encouraged the deployment of various network applications that are rich with multimedia and real-time services. These services demand stringent requirements are defined through Quality of Service (QoS) parameters such as delay, jitter, loss, etc. To guarantee the delivery of these services QoS routing algorithms that deal with multiple metrics are needed. Unfortunately, QoS routing with multiple metrics is considered an NP-complete problem that cannot be solved by a simple algorithm. This paper proposes three source based QoS routing algorithms that find the optimal path from the service provider to the user that best satisfies the QoS requirements for a particular service. The three algorithms use the same filtering technique to prune all the paths that do not meet the requirements which solves the complexity of NP-complete problem. Next, each of the three algorithms integrates a different Multiple Criteria Decision Making method to select one of the paths that have resulted from the route filtering technique. The three decision making methods used are the Analytic Hierarchy Process (AHP), Multi-Attribute Utility Theory (MAUT), and Kepner-Tregoe KT. Results show that the algorithms find a path using multiple constraints with a high ability to handle multimedia and real-time applications.

Towards Efficient Bounds on Completion Time and Resource Provisioning for Scheduling Workflows on Heterogeneous Processing Systems

2017 ◽  
Vol 9 (3) ◽  
pp. 60-82 ◽  
Author(s):  
D. Sirisha ◽  
G. Vijayakumari
Keyword(s):  
Completion Time ◽  
High Performance ◽  
Turnaround Time ◽  
Resource Provisioning ◽  
Optimal Solutions ◽  
Complete Problem ◽  
Heterogeneous Processing ◽  
Heuristic Scheduling ◽  
Np Complete ◽  
Workflow Tasks

Compute intensive applications featured as workflows necessitate Heterogeneous Processing Systems (HPS) for attaining high performance to minimize the turnaround time. Efficient scheduling of the workflow tasks is paramount to attain higher potentials of HPS and is a challenging NP-Complete problem. In the present work, Branch and Bound (BnB) strategy is applied to optimally schedule the workflow tasks. The proposed bounds are tighter, simpler and less complex than the existing bounds and the upper bound is closer to the exact solution. Moreover, the bounds on the resource provisioning are devised to execute the workflows in the minimum possible time and optimally utilize the resources. The performance of the proposed BnB strategy is evaluated on a suite of benchmark workflows. The experimental results reveal that the proposed BnB strategy improved the optimal solutions compared to the existing heuristic scheduling algorithms for more than 20 percent of the cases and generated better schedules over 7 percent for 82.6 percent of the cases.

scholarly journals aspBEEF: Explaining Predictions Through Optimal Clustering

Proceedings ◽  
2020 ◽  
Vol 54 (1) ◽  
pp. 51
Author(s):  
Pedro Cabalar ◽  
Rodrigo Martín ◽  
Brais Muñiz ◽  
Gilberto Pérez
Keyword(s):  
Machine Learning ◽  
Answer Set Programming ◽  
Programming Paradigm ◽  
Learning Classifier ◽  
Np Complete ◽  
Np Problems ◽  
Answer Set

In this paper we introduce aspBEEF, a tool for generating explanations for the outcome of an arbitrary machine learning classifier. This is done using Grover’s et al. framework known as Balanced English Explanations of Forecasts (BEEF) that generates explanations in terms of in terms of finite intervals over the values of the input features. Since the problem of obtaining an optimal BEEF explanation has been proved to be NP-complete, BEEF existing implementation computes an approximation. In this work we use instead an encoding into the Answer Set Programming paradigm, specialized in solving NP problems, to guarantee that the computed solutions are optimal.

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