scholarly journals A New Distributed Approximation Algorithm for the Maximum Weight Independent Set Problem

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Peng Du ◽  
Yuan Zhang
Keyword(s):  
Optimization Problem ◽  
Optimal Solution ◽  
Independent Set ◽  
Wireless Networking ◽  
Combinatorial Optimization Problem ◽  
Maximum Weight ◽  
Approximation Accuracy ◽  
Maximum Weight Independent Set ◽  
Convergence Performance ◽  
Distributed Approximation

Maximum weight independent set (MWIS) is a combinatorial optimization problem that naturally arises in many applications especially wireless networking. This paper studies distributed approximation algorithms for finding MWIS in a general graph. In the proposed algorithm, each node keeps exchanging messages with neighbors in which each message contains partial solutions of the MWIS optimization program. A parameterHis introduced to achieve different tradeoff between approximation accuracy and space complexity. Theoretical analysis shows that the proposed algorithm is guaranteed to converge to an approximate solution after finite iterations; specifically, the proposed algorithm is guaranteed to converge to the optimal solution withH=+∞. Simulation results confirm the effectiveness of the proposed distributed algorithm in terms of weight sum, message size, and convergence performance.

scholarly journals Quit When You Can: Efficient Evaluation of Ensembles by Optimized Ordering

2021 ◽  
Vol 17 (4) ◽  
pp. 1-20
Author(s):  
Serena Wang ◽  
Maya Gupta ◽  
Seungil You
Keyword(s):  
Optimization Problem ◽  
Optimal Solution ◽  
Combinatorial Optimization Problem ◽  
Joint Optimization ◽  
Early Stopping ◽  
Time Approximation ◽  
Approximation Bound ◽  
Evaluation Time ◽  
Speed Up ◽  
Real World Problems

Given a classifier ensemble and a dataset, many examples may be confidently and accurately classified after only a subset of the base models in the ensemble is evaluated. Dynamically deciding to classify early can reduce both mean latency and CPU without harming the accuracy of the original ensemble. To achieve such gains, we propose jointly optimizing the evaluation order of the base models and early-stopping thresholds. Our proposed objective is a combinatorial optimization problem, but we provide a greedy algorithm that achieves a 4-approximation of the optimal solution under certain assumptions, which is also the best achievable polynomial-time approximation bound. Experiments on benchmark and real-world problems show that the proposed Quit When You Can (QWYC) algorithm can speed up average evaluation time by 1.8–2.7 times on even jointly trained ensembles, which are more difficult to speed up than independently or sequentially trained ensembles. QWYC’s joint optimization of ordering and thresholds also performed better in experiments than previous fixed orderings, including gradient boosted trees’ ordering.

scholarly journals New Instances for Maximum Weight Independent Set From a Vehicle Routing Application

2021 ◽  
Vol 2 (4) ◽  
Author(s):  
Yuanyuan Dong ◽  
Andrew V. Goldberg ◽  
Alexander Noe ◽  
Nikos Parotsidis ◽  
Mauricio G. C. Resende ◽  
...  
Keyword(s):  
Vehicle Routing ◽  
Real World ◽  
Vehicle Routing Problem ◽  
Independent Set ◽  
Maximum Weight ◽  
Routing Problem ◽  
Independent Set Problem ◽  
Maximum Weight Independent Set ◽  
Large Size

AbstractWe present a set of new instances of the maximum weight independent set problem. These instances are derived from a real-world vehicle routing problem and are challenging to solve in part because of their large size. We present instances with up to 881 thousand nodes and 383 million edges.

An Approximate Algorithm for Triangle TSP with a Four-Vertex-Three-Line Inequality

2015 ◽  
Vol 6 (1) ◽  
pp. 35-46 ◽  
Author(s):  
Yong Wang
Keyword(s):  
Time Complexity ◽  
Optimization Problem ◽  
Nearest Neighbor ◽  
Optimal Solution ◽  
Simple Algorithm ◽  
Exact Algorithms ◽  
Combinatorial Optimization Problem ◽  
Traveling Salesman ◽  
Approximate Algorithm ◽  
Nearest Neighbor Algorithm

Traveling salesman problem (TSP) is a classic combinatorial optimization problem. The time complexity of the exact algorithms is generally an exponential function of the scale of TSP. This work gives an approximate algorithm with a four-vertex-three-line inequality for the triangle TSP. The time complexity is O(n2) and it can generate an approximation less than 2 times of the optimal solution. The paper designs a simple algorithm with the inequality. The algorithm is compared with the double-nearest neighbor algorithm. The experimental results illustrate the algorithm find the better approximations than the double-nearest neighbor algorithm for most TSP instances.

scholarly journals Solving the Set Packing Problem via a Maximum Weighted Independent Set Heuristic

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Ruizhi Li ◽  
Yupan Wang ◽  
Shuli Hu ◽  
Jianhua Jiang ◽  
Dantong Ouyang ◽  
...  
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problem ◽  
State Of The Art ◽  
Independent Set ◽  
Packing Problem ◽  
Combinatorial Optimization Problem ◽  
Set Packing ◽  
Benchmark Instances ◽  
Set Packing Problem

The set packing problem (SPP) is a significant NP-hard combinatorial optimization problem with extensive applications. In this paper, we encode the set packing problem as the maximum weighted independent set (MWIS) problem and solve the encoded problem with an efficient algorithm designed to the MWIS problem. We compare the independent set-based method with the state-of-the-art algorithms for the set packing problem on the 64 standard benchmark instances. The experimental results show that the independent set-based method is superior to the existing algorithms in terms of the quality of the solutions and running time obtained the solutions.

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