Complexity and inapproximability results for Balanced Connected Subgraph Problem

2021 ◽  
Author(s):  
T. Martinod ◽  
V. Pollet ◽  
B. Darties ◽  
R. Giroudeau ◽  
J.-C. König
Keyword(s):  
Connected Subgraph

Approximate Mining of Frequent -Subgraph Patterns in Evolving Graphs

2021 ◽  
Vol 15 (3) ◽  
pp. 1-35
Author(s):  
Muhammad Anis Uddin Nasir ◽  
Cigdem Aslay ◽  
Gianmarco De Francisci Morales ◽  
Matteo Riondato
Keyword(s):  
Sample Size ◽  
State Of The Art ◽  
Empirical Evaluation ◽  
Connected Subgraph ◽  
Dynamic Graphs ◽  
High Quality ◽  
Complexity Bounds ◽  
Approximation Quality ◽  
Uniform Sample ◽  
Waiting For Godot

“Perhaps he could dance first and think afterwards, if it isn’t too much to ask him.” S. Beckett, Waiting for Godot Given a labeled graph, the collection of -vertex induced connected subgraph patterns that appear in the graph more frequently than a user-specified minimum threshold provides a compact summary of the characteristics of the graph, and finds applications ranging from biology to network science. However, finding these patterns is challenging, even more so for dynamic graphs that evolve over time, due to the streaming nature of the input and the exponential time complexity of the problem. We study this task in both incremental and fully-dynamic streaming settings, where arbitrary edges can be added or removed from the graph. We present TipTap , a suite of algorithms to compute high-quality approximations of the frequent -vertex subgraphs w.r.t. a given threshold, at any time (i.e., point of the stream), with high probability. In contrast to existing state-of-the-art solutions that require iterating over the entire set of subgraphs in the vicinity of the updated edge, TipTap operates by efficiently maintaining a uniform sample of connected -vertex subgraphs, thanks to an optimized neighborhood-exploration procedure. We provide a theoretical analysis of the proposed algorithms in terms of their unbiasedness and of the sample size needed to obtain a desired approximation quality. Our analysis relies on sample-complexity bounds that use Vapnik–Chervonenkis dimension, a key concept from statistical learning theory, which allows us to derive a sufficient sample size that is independent from the size of the graph. The results of our empirical evaluation demonstrates that TipTap returns high-quality results more efficiently and accurately than existing baselines.

scholarly journals Colorings of (r, r)-Uniform, Complete, Circular, Mixed Hypergraphs

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 828
Author(s):  
Nicholas Newman ◽  
Vitaly Voloshin
Keyword(s):  
Block Designs ◽  
Connected Subgraph ◽  
Vertex Set ◽  
Mixed Hypergraph

In colorings of some block designs, the vertices of blocks can be thought of as hyperedges of a hypergraph H that can be placed on a circle and colored according to some rules that are related to colorings of circular mixed hypergraphs. A mixed hypergraph H is called circular if there exists a host cycle on the vertex set X such that every edge (C- or D-) induces a connected subgraph of this cycle. We propose an algorithm to color the (r,r)-uniform, complete, circular, mixed hypergraphs for all feasible values with no gaps. In doing so, we show χ(H)=2 and χ¯(H)=n−s or n−s−1 where s is the sieve number.

scholarly journals Small world and stability analysis of industrial coupling symbiosis network of ecological industrial park of oil and gas resource cities

2021 ◽  
pp. 014459872098361
Author(s):  
Yanqiu Wang ◽  
Zhengxin Sun ◽  
Pengtai Li ◽  
Zhiwei Zhu
Keyword(s):  
System Analysis ◽  
Oil And Gas ◽  
Small World ◽  
Industrial Park ◽  
Sharp Change ◽  
Connected Subgraph ◽  
Network Efficiency ◽  
Complex Network Theory ◽  
The Stability ◽  
Agglomeration Coefficient

This paper analyzes the small cosmopolitan and stability of the industrial coupling symbiotic network of eco-industrial parks of oil and gas resource-based cities. Taking Daqing A Ecological Industrial Park as an example, we constructed the characteristic index system and calculated the topological parameters such as the agglomeration coefficient and the average shortest path length of the industrial coupling symbiotic network. Based on the complex network theory we analyzed the characteristics of the scaled world, constructed the adjacency matrix of material and information transfers between enterprises, drew the network topology diagram. We simulated the system analysis and analyzed the stability of the industrial coupling symbiotic network of the eco-industrial park using the network efficiency and node load and maximum connected subgraph. The analysis results are as follows: the small world degree δ of Daqing A Eco-industrial Park is 0.891, which indicates that the industrial coupled symbiotic network has strong small world characteristics; the average path is 1.268, and the agglomeration coefficient is 0.631. The probability of edge connection between two nodes in a symbiotic network is 63.1%, which has a relatively high degree of aggregation, indicating that energy and material exchanges are frequent among all enterprises in the network, the degree of network aggregation is high, and the dependence between nodes is high; when the tolerance parameter is 0 to 0.3, the network efficiency and the maximum connected subgraphs show a sharp change trend, indicating that the topology of the industrial coupling symbiotic network of the eco-industrial park changes drastically when the network is subjected to deliberate attacks. It is easy to cause the breakage of material flow and energy flow in the industrial park, which leads to the decline of the stability of the industrial coupling symbiotic network of the eco-industrial park.

scholarly journals A Fast and Exact Greedy Algorithm for the Core–Periphery Problem

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 94 ◽  
Author(s):  
Dario Fasino ◽  
Franca Rinaldi
Keyword(s):  
Structural Analysis ◽  
Optimization Problem ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Combinatorial Optimization Problem ◽  
Connected Subgraph ◽  
Optimal Solutions ◽  
The Core ◽  
Core Set ◽  
Key Concepts

The core–periphery structure is one of the key concepts in the structural analysis of complex networks. It consists of a partitioning of the node set of a given graph or network into two groups, called core and periphery, where the core nodes induce a well-connected subgraph and share connections with peripheral nodes, while the peripheral nodes are loosely connected to the core nodes and other peripheral nodes. We propose a polynomial-time algorithm to detect core–periphery structures in networks having a symmetric adjacency matrix. The core set is defined as the solution of a combinatorial optimization problem, which has a pleasant symmetry with respect to graph complementation. We provide a complete description of the optimal solutions to that problem and an exact and efficient algorithm to compute them. The proposed approach is extended to networks with loops and oriented edges. Numerical simulations are carried out on both synthetic and real-world networks to demonstrate the effectiveness and practicability of the proposed algorithm.

scholarly journals Minimum Cost ≤k Edges Connected Subgraph Problems

2010 ◽  
Vol 36 ◽  
pp. 25-32 ◽  
Author(s):  
Firdovsi Sharifov ◽  
Hakan Kutucu
Keyword(s):  
Minimum Cost ◽  
Connected Subgraph

Analysis of Identification Methods of Key Nodes in Transportation Network

2022 ◽  
Author(s):  
Qiang Lai ◽  
Hong-hao Zhang
Keyword(s):  
Transportation Networks ◽  
Transportation Network ◽  
Practical Significance ◽  
Node Degree ◽  
Connected Subgraph ◽  
Network Efficiency ◽  
Identification Methods ◽  
Identification Method ◽  
Bus Networks ◽  
Key Nodes

Abstract The identification of key nodes plays an important role in improving the robustness of the transportation network. For different types of transportation networks, the effect of the same identification method may be different. It is of practical significance to study the key nodes identification methods corresponding to various types of transportation networks. Based on the knowledge of complex networks, the metro networks and the bus networks are selected as the objects, and the key nodes are identified by the node degree identification method, the neighbor node degree identification method, the weighted k-shell degree neighborhood identification method (KSD), the degree k-shell identification method (DKS), and the degree k-shell neighborhood identification method (DKSN). Take the network efficiency and the largest connected subgraph as the effective indicators. The results show that the KSD identification method that comprehensively considers the elements has the best recognition effect and has certain practical significance.

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