Enumerating Connected Subgraphs and Computing the Myerson and Shapley Values in Graph-Restricted Games

2019 ◽  
Vol 10 (2) ◽  
pp. 1-25 ◽  
Author(s):  
Oskar Skibski ◽  
Talal Rahwan ◽  
Tomasz P. Michalak ◽  
Michael Wooldridge
Keyword(s):  
Shapley Values ◽  
Connected Subgraphs ◽  
Restricted Games

ON THE COMPLEXITY OF COMPUTING VALUES OF RESTRICTED GAMES

2002 ◽  
Vol 13 (05) ◽  
pp. 633-651 ◽  
Author(s):  
J. M. BILBAO ◽  
J. R. FERNÁNDEZ ◽  
J. J. LÓPEZ
Keyword(s):  
Cooperative Games ◽  
Partially Ordered Set ◽  
Polynomial Algorithm ◽  
Ordered Set ◽  
Combinatorial Structure ◽  
Distributive Lattices ◽  
Communication Graph ◽  
Partially Ordered ◽  
Connected Subgraphs ◽  
Restricted Games

The aim of this paper is to compute Shapley's and Banzhaf's values of cooperative games restricted by a combinatorial structure. There have been previous models developed to study the problem of games with partial cooperation. Games restricted by a communication graph were introduced by Myerson and Owen. Another type of combinatorial structure introduced by Gilles, Owen and van den Brink is equivalent to a subclass of antimatroids. Cooperative games in which the set of players is a partially ordered set, that is, games on distributive lattices was investigated by Faigle and Kern. We introduce a new combinatorial structure called augmenting system which is a generaligation of the antimatroid structure and the system of connected subgraphs of graph. We present new algorithmic procedures for computing values of games under augmenting systems restrictions and we show that there exist problems with polynomial algorithm complexity.

A novel q-rung orthopair fuzzy TODIM approach for multi-criteria group decision making based on Shapley value and relative entropy

2021 ◽  
Vol 40 (1) ◽  
pp. 235-250
Author(s):  
Liuxin Chen ◽  
Nanfang Luo ◽  
Xiaoling Gou
Keyword(s):  
Decision Making ◽  
Relative Entropy ◽  
Group Decision Making ◽  
Shapley Value ◽  
Group Decision ◽  
Similarity Measures ◽  
Entropy Measure ◽  
Shapley Values ◽  
Interactive Relationship ◽  
The Difference

In the real multi-criteria group decision making (MCGDM) problems, there will be an interactive relationship among different decision makers (DMs). To identify the overall influence, we define the Shapley value as the DM’s weight. Entropy is a measure which makes it better than similarity measures to recognize a group decision making problem. Since we propose a relative entropy to measure the difference between two systems, which improves the accuracy of the distance measure.In this paper, a MCGDM approach named as TODIM is presented under q-rung orthopair fuzzy information.The proposed TODIM approach is developed for correlative MCGDM problems, in which the weights of the DMs are calculated in terms of Shapley values and the dominance matrices are evaluated based on relative entropy measure with q-rung orthopair fuzzy information.Furthermore, the efficacy of the proposed Gq-ROFWA operator and the novel TODIM is demonstrated through a selection problem of modern enterprises risk investment. A comparative analysis with existing methods is presented to validate the efficiency of the approach.

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.

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