scholarly journals Efficient constructions of convex combinations for 2-edge-connected subgraphs on fundamental classes

2021 ◽  
Vol 42 ◽  
pp. 100659
Author(s):  
Arash Haddadan ◽  
Alantha Newman
Keyword(s):  
Connected Subgraphs

scholarly journals Faster Motif Counting via Succinct Color Coding and Adaptive Sampling

2021 ◽  
Vol 15 (6) ◽  
pp. 1-27
Author(s):  
Marco Bressan ◽  
Stefano Leucci ◽  
Alessandro Panconesi
Keyword(s):  
Adaptive Sampling ◽  
Relative Frequency ◽  
State Of The Art ◽  
Color Coding ◽  
Input Graph ◽  
Large Graphs ◽  
Running Time ◽  
Uniform Sampling ◽  
Current State ◽  
Connected Subgraphs

We address the problem of computing the distribution of induced connected subgraphs, aka graphlets or motifs , in large graphs. The current state-of-the-art algorithms estimate the motif counts via uniform sampling by leveraging the color coding technique by Alon, Yuster, and Zwick. In this work, we extend the applicability of this approach by introducing a set of algorithmic optimizations and techniques that reduce the running time and space usage of color coding and improve the accuracy of the counts. To this end, we first show how to optimize color coding to efficiently build a compact table of a representative subsample of all graphlets in the input graph. For 8-node motifs, we can build such a table in one hour for a graph with 65M nodes and 1.8B edges, which is times larger than the state of the art. We then introduce a novel adaptive sampling scheme that breaks the “additive error barrier” of uniform sampling, guaranteeing multiplicative approximations instead of just additive ones. This allows us to count not only the most frequent motifs, but also extremely rare ones. For instance, on one graph we accurately count nearly 10.000 distinct 8-node motifs whose relative frequency is so small that uniform sampling would literally take centuries to find them. Our results show that color coding is still the most promising approach to scalable motif counting.

scholarly journals A novel algorithm for finding top-k weighted overlapping densest connected subgraphs in dual networks

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Riccardo Dondi ◽  
Mohammad Mehdi Hosseinzadeh ◽  
Pietro H. Guzzi
Keyword(s):  
Complex Systems ◽  
Physical Network ◽  
Conceptual Network ◽  
Connected Subgraphs ◽  
Novel Algorithm

AbstractThe use of networks for modelling and analysing relations among data is currently growing. Recently, the use of a single networks for capturing all the aspects of some complex scenarios has shown some limitations. Consequently, it has been proposed to use Dual Networks (DN), a pair of related networks, to analyse complex systems. The two graphs in a DN have the same set of vertices and different edge sets. Common subgraphs among these networks may convey some insights about the modelled scenarios. For instance, the detection of the Top-k Densest Connected subgraphs, i.e. a set k subgraphs having the largest density in the conceptual network which are also connected in the physical network, may reveal set of highly related nodes. After proposing a formalisation of the approach, we propose a heuristic to find a solution, since the problem is computationally hard. A set of experiments on synthetic and real networks is also presented to support our approach.

A Novel Symbolic OBDD Algorithm for Generating Mechanical Assembly Sequences Using Decomposition Approach

2011 ◽  
Vol 201-203 ◽  
pp. 24-29
Author(s):  
Zhou Bo Xu ◽  
Tian Long Gu ◽  
Liang Chang ◽  
Feng Ying Li
Keyword(s):  
Assembly Sequence Planning ◽  
The Novel ◽  
Mechanical Assembly ◽  
Breadth First Search ◽  
Decomposition Approach ◽  
Translation Function ◽  
Assembly Sequences ◽  
Cut Set ◽  
Connected Subgraphs ◽  
Induced Graph

The compact storage and efficient evaluation of feasible assembly sequences is one crucial concern for assembly sequence planning. The implicitly symbolic ordered binary decision diagram (OBDD) representation and manipulation technique has been a promising way. In this paper, Sharafat’s recursive contraction algorithm and cut-set decomposition method are symbolically implemented, and a novel symbolic algorithm for generating mechanical assembly sequences is presented using OBDD formulations of liaison graph and translation function. The algorithm has the following main procedures: choosing any one of vertices in the liaison graph G as seed vertex and scanning all connected subgraphs containing seed vertex by breadth first search; transforming the problem of enumerating all cut-sets in liaison graph into the problem of generating all the partitions: two subsets V1and V2of a set of vertices V where both the induced graph of vertices V1and V2are connected; checking the geometrical feasibility for each cut-set. Some applicable experiments show that the novel algorithm can generate feasible assembly sequences correctly and completely.

On Finding Minimal Two-Connected Subgraphs

1995 ◽  
Vol 18 (1) ◽  
pp. 1-49 ◽  
Author(s):  
P. Kelsen ◽  
V. Ramachandran
Keyword(s):  
Connected Subgraphs

scholarly journals Graphs with most number of three point induced connected subgraphs

1995 ◽  
Vol 59 (1) ◽  
pp. 1-10 ◽  
Author(s):  
F.T. Boesch ◽  
X. Li ◽  
J. Rodriguez
Keyword(s):  
Connected Subgraphs

scholarly journals Rooted $K_4$-Minors

10.37236/3476 ◽  
2013 ◽  
Vol 20 (2) ◽  
Author(s):  
Ruy Fabila-Monroy ◽  
David R. Wood
Keyword(s):  
Planar Graph ◽  
Pairwise Disjoint ◽  
Single Face ◽  
Special Cases ◽  
Connected Subgraphs ◽  
Connected Planar Graph

Let $a,b,c,d$ be four vertices in a graph $G$. A $K_4$ minor rooted at $a,b,c,d$ consists of four pairwise-disjoint pairwise-adjacent connected subgraphs of $G$, respectively containing $a,b,c,d$. We characterise precisely when $G$ contains a $K_4$-minor rooted at $a,b,c,d$ by describing six classes of obstructions, which are the edge-maximal graphs containing no $K_4$-minor rooted at $a,b,c,d$. The following two special cases illustrate the full characterisation: (1) A 4-connected non-planar graph contains a $K_4$-minor rooted at $a,b,c,d$ for every choice of $a,b,c,d$. (2) A 3-connected planar graph contains a $K_4$-minor rooted at $a,b,c,d$ if and only if $a,b,c,d$ are not on a single face.

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