An Approximation Algorithm for a Semi-supervised Graph Clustering Problem

2020 ◽  
pp. 23-29
Author(s):  
Victor Il’ev ◽  
Svetlana Il’eva ◽  
Alexander Morshinin
Keyword(s):  
Approximation Algorithm ◽  
Graph Clustering ◽  
Clustering Problem

A local search for a graph clustering problem

2016 ◽  
Author(s):  
Anna Navrotskaya ◽  
Victor Il’ev
Keyword(s):  
Local Search ◽  
Graph Clustering ◽  
Clustering Problem

APPROXIMATE ALGORITHMS FOR GRAPH CLUSTERING PROBLEM

2019 ◽  
pp. 64-77
Author(s):  
V. P. Il’ev ◽  
◽  
S. D. Il’eva ◽  
A. V. Morshinin ◽  
◽  
...  
Keyword(s):  
Graph Clustering ◽  
Approximate Algorithms ◽  
Clustering Problem

The graph clustering problem has a perfect zero-knowledge interactive proof

1999 ◽  
Vol 69 (4) ◽  
pp. 201-206 ◽  
Author(s):  
Alfredo De Santis ◽  
Giovanni Di Crescenzo ◽  
Oded Goldreich ◽  
Giuseppe Persiano
Keyword(s):  
Graph Clustering ◽  
Interactive Proof ◽  
Zero Knowledge ◽  
Clustering Problem

A BETTER APPROXIMATION FOR MINIMUM AVERAGE ROUTING PATH CLUSTERING PROBLEM IN 2-D UNDERWATER SENSOR NETWORKS

2009 ◽  
Vol 01 (02) ◽  
pp. 175-191 ◽  
Author(s):  
WEI WANG ◽  
DONGHYUN KIM ◽  
JAMES WILLSON ◽  
BHAVANI THURAISINGHAM ◽  
WEILI WU
Keyword(s):  
Sensor Networks ◽  
Approximation Algorithm ◽  
Dominating Set ◽  
Minimum Weight ◽  
Performance Ratio ◽  
Underwater Sensor Networks ◽  
Clustering Problem ◽  
Np Completeness ◽  
Dominating Set Problem ◽  
Special Case

Previously, we proposed Minimum Average Routing Path Clustering Problem (MARPCP) in multi-hop USNs. The goal of this problem is to find a clustering of a USN so that the average clustering-based routing path from a node to it nearest underwater sink is minimized. We relaxed MARPCP to a special case of Minimum Weight Dominating Set Problem (MWDSP), namely MWDSP-R. In addition, we showed the Performance Ratio (PR) of α-approximation algorithm for MWDSP-R is 3α for MARPCP. Based on this result, we showed the existence of a (15 + ∊)-approximation algorithm for MARPCP. In this paper, we first establish the NP-completeness of both MARPCP and MWDSP-R. Then, we propose a PTAS for MWDSP-R. By combining this result with our previous one, we have a (3 + ∊)-approximation algorithm for MARPCP.

scholarly journals Market Graph Clustering via QUBO and Digital Annealing

2021 ◽  
Vol 14 (1) ◽  
pp. 34
Author(s):  
Seo Woo Hong ◽  
Pierre Miasnikof ◽  
Roy Kwon ◽  
Yuri Lawryshyn
Keyword(s):  
Graph Clustering ◽  
Small Subset ◽  
Index Tracking ◽  
Np Hard ◽  
Tracking Problem ◽  
Financial Industry ◽  
Graph Models ◽  
Clustering Problem ◽  
Market Graph ◽  
Common Task

We present a novel technique for cardinality-constrained index-tracking, a common task in the financial industry. Our approach is based on market graph models. We model our reference indices as market graphs and express the index-tracking problem as a quadratic K-medoids clustering problem. We take advantage of a purpose-built hardware architecture to circumvent the NP-hard nature of the problem and solve our formulation efficiently. The main contributions of this article are bridging three separate areas of the literature, market graph models, K-medoid clustering and quadratic binary optimization modeling, to formulate the index-tracking problem as a binary quadratic K-medoid graph-clustering problem. Our initial results show we accurately replicate the returns of various market indices, using only a small subset of their constituent assets. Moreover, our binary quadratic formulation allows us to take advantage of recent hardware advances to overcome the NP-hard nature of the problem and obtain solutions faster than with traditional architectures and solvers.

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