GRAPH BISECTION MODELED AS CARDINALITY CONSTRAINED BINARY QUADRATIC TASK ALLOCATION

2013 ◽  
Vol 12 (02) ◽  
pp. 261-276 ◽  
Author(s):  
MARK LEWIS ◽  
GARY KOCHENBERGER
Keyword(s):  
Task Allocation ◽  
Graph Partitioning ◽  
State Of The Art ◽  
Quadratic Model ◽  
Complete Problem ◽  
Binary Model ◽  
Comparison Results ◽  
Graph Bisection ◽  
Strategic Oscillation ◽  
Np Complete

In this paper, the cardinality constrained quadratic model for binary quadratic programming is used to model and solve the graph bisection problem as well as its generalization in the form of the task allocation problem with two processors (2-TAP). Balanced graph bisection is an NP-complete problem which partitions a set of nodes in the graph G = (N, E) into two sets with equal cardinality such that a minimal sum of edge weights exists between the nodes in the two separate sets. 2-TAP is graph bisection with the addition of node preference costs in the objective function. We transform the general linear k-TAP model to the cardinality constrained quadratic binary model so that it may be efficiently solved using tabu search with strategic oscillation. On a set of benchmark graph bisections, we improve the best known solution for several problems. Comparison results with the state-of-the-art graph partitioning program METIS, as well as Cplex and Gurobi are presented on a set of randomly generated graphs. This approach is shown to also work well with 2-TAP, comparing favorably to Cplex and Gurobi, providing better solutions in a much shorter time.

scholarly journals DHPV: A Distributed Algorithm for Large-Scale Graph Partitioning

2020 ◽  
Author(s):  
Wilfried Yves Hamilton Adoni ◽  
Tarik Nahhal ◽  
Moez Krichen ◽  
Abdeltif El byed ◽  
Ismail Assayad
Keyword(s):  
Graph Partitioning ◽  
Distributed Algorithm ◽  
Large Scale ◽  
Data Exploration ◽  
Significant Gain ◽  
Complete Problem ◽  
Big Graph ◽  
Big Graphs ◽  
Strongly Connected ◽  
Np Complete

Abstract Big graphs are part of the movement of "Not Only SQL" databases (also called NoSQL) focusing on the relationships between data, rather than the values themselves. The data is stored in vertices while the edges model the interactions or relationships between these data. They offer flexibility in handling data that is strongly connected to each other. The analysis of a big graph generally involves exploring all of its vertices. Thus, this operation is costly in time and resources because big graphs are generally composed of millions of vertices connected through billions of edges. Consequently, the graph algorithms are expansive compared to the size of the big graph, and are therefore ineffective for data exploration. Thus, partitioning the graph stands out as an efficient and less expensive alternative for exploring a big graph. This technique consists in partitioning the graph into a set of k sub-graphs in order to reduce the complexity of the queries. Nevertheless, it presents many challenges because it is an NP-complete problem. In this article, we present DPHV (Distributed Placement of Hub-Vertices) an efficient parallel and distributed heuristic for large-scale graph partitioning. An application on a real-world graphs demonstrates the feasibility and reliability of our method. The experiments carried on a 10-nodes Spark cluster proved that the proposed methodology achieves significant gain in term of time and outperforms JA-BE-JA, Greedy, DFEP.

scholarly journals DHPV: A Distributed Algorithm for Large-Scale Graph Partitioning

2020 ◽  
Author(s):  
Wilfried Yves Hamilton Adoni ◽  
Tarik Nahhal ◽  
Moez Krichen ◽  
Abdeltif El byed ◽  
Ismail Assayad
Keyword(s):  
Graph Partitioning ◽  
Distributed Algorithm ◽  
Large Scale ◽  
Data Exploration ◽  
Significant Gain ◽  
Complete Problem ◽  
Big Graph ◽  
Big Graphs ◽  
Strongly Connected ◽  
Np Complete

Abstract Big graphs are part of the movement of "Not Only SQL" databases (also called NoSQL) focusing on the relationships between data, rather than the values themselves. The data is stored in vertices while the edges model the interactions or relationships between these data. They offer flexibility in handling data that is strongly connected to each other. The analysis of a big graph generally involves exploring all of its vertices. Thus, this operation is costly in time and resources because big graphs are generally composed of millions of vertices connected through billions of edges. Consequently, the graph algorithms are expansive compared to the size of the big graph, and are therefore ineffective for data exploration. Thus, partitioning the graph stands out as an efficient and less expensive alternative for exploring a big graph. This technique consists in partitioning the graph into a set of k sub-graphs in order to reduce the complexity of the queries. Nevertheless, it presents many challenges because it is an NP-complete problem. In this article, we present DPHV (Distributed Placement of Hub-Vertices) an efficient parallel and distributed heuristic for large-scale graph partitioning. An application on a real-world graphs demonstrates the feasibility and reliability of our method. The experiments carried on a 10-nodes Spark cluster proved that the proposed methodology achieves significant gain in term of time and outperforms JA-BE-JA, Greedy, DFEP

scholarly journals ODSS: Efficient Hybridization for Optimal Coalition Structure Generation

2020 ◽  
Vol 34 (05) ◽  
pp. 7079-7086
Author(s):  
Narayan Changder ◽  
Samir Aknine ◽  
Sarvapali Ramchurn ◽  
Animesh Dutta
Keyword(s):  
Hybrid Algorithm ◽  
State Of The Art ◽  
Coalition Structure ◽  
Search Space ◽  
The State ◽  
Structure Generation ◽  
Complete Problem ◽  
Disjoint Sets ◽  
Np Complete ◽  
Coalition Structure Generation

Coalition Structure Generation (CSG) is an NP-complete problem that remains difficult to solve on account of its complexity. In this paper, we propose an efficient hybrid algorithm for optimal coalition structure generation called ODSS. ODSS is a hybrid version of two previously established algorithms IDP (Rahwan and Jennings 2008) and IP (Rahwan et al. 2009). ODSS minimizes the overlapping between IDP and IP by dividing the whole search space of CSG into two disjoint sets of subspaces and proposes a novel subspace shrinking technique to reduce the size of the subspace searched by IP with the help of IDP. When compared to the state-of-the-art against a wide variety of value distributions, ODSS is shown to perform better by up to 54.15% on benchmark inputs.

scholarly journals DHPV: a distributed algorithm for large-scale graph partitioning

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Wilfried Yves Hamilton Adoni ◽  
Tarik Nahhal ◽  
Moez Krichen ◽  
Abdeltif El byed ◽  
Ismail Assayad
Keyword(s):  
Graph Partitioning ◽  
Distributed Algorithm ◽  
Large Scale ◽  
Data Exploration ◽  
Significant Gain ◽  
Complete Problem ◽  
Big Graph ◽  
Big Graphs ◽  
Strongly Connected ◽  
Np Complete

Abstract Big graphs are part of the movement of “Not Only SQL” databases (also called NoSQL) focusing on the relationships between data, rather than the values themselves. The data is stored in vertices while the edges model the interactions or relationships between these data. They offer flexibility in handling data that is strongly connected to each other. The analysis of a big graph generally involves exploring all of its vertices. Thus, this operation is costly in time and resources because big graphs are generally composed of millions of vertices connected through billions of edges. Consequently, the graph algorithms are expansive compared to the size of the big graph, and are therefore ineffective for data exploration. Thus, partitioning the graph stands out as an efficient and less expensive alternative for exploring a big graph. This technique consists in partitioning the graph into a set of k sub-graphs in order to reduce the complexity of the queries. Nevertheless, it presents many challenges because it is an NP-complete problem. In this article, we present DPHV (Distributed Placement of Hub-Vertices) an efficient parallel and distributed heuristic for large-scale graph partitioning. An application on a real-world graphs demonstrates the feasibility and reliability of our method. The experiments carried on a 10-nodes Spark cluster proved that the proposed methodology achieves significant gain in term of time and outperforms JA-BE-JA, Greedy, DFEP.

scholarly journals A Hybrid Strategic Oscillation with Path Relinking Algorithm for the Multiobjective k-Balanced Center Location Problem

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 853
Author(s):  
Jesús Sánchez-Oro ◽  
Ana D. López-Sánchez ◽  
Anna Martínez-Gavara ◽  
Alfredo G. Hernández-Díaz ◽  
Abraham Duarte
Keyword(s):  
Location Problem ◽  
State Of The Art ◽  
Path Relinking ◽  
Multiobjective Evolutionary Algorithms ◽  
Demand Point ◽  
High Quality ◽  
Nondominated Solutions ◽  
Center Location ◽  
Strategic Oscillation ◽  
N Demand

This paper presents a hybridization of Strategic Oscillation with Path Relinking to provide a set of high-quality nondominated solutions for the Multiobjective k-Balanced Center Location problem. The considered location problem seeks to locate k out of m facilities in order to serve n demand points, minimizing the maximum distance between any demand point and its closest facility while balancing the workload among the facilities. An extensive computational experimentation is carried out to compare the performance of our proposal, including the best method found in the state-of-the-art as well as traditional multiobjective evolutionary algorithms.

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
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