Learning-Based Approaches for Graph Problems: A Survey

Over the years, many graph problems specifically those in NP-complete are studied by a wide range of researchers. Some famous examples include graph colouring, travelling salesman problem and subgraph isomorphism. Most of these problems are typically addressed by exact algorithms, approximate algorithms and heuristics. There are however some drawback for each of these methods. Recent studies have employed learning-based frameworks such as machine learning techniques in solving these problems, given that they are useful in discovering new patterns in structured data that can be represented using graphs. This research direction has successfully attracted a considerable amount of attention. In this survey, we provide a systematic review mainly on classic graph problems in which learning-based approaches have been proposed in addressing the problems. We discuss the overview of each framework, and provide analyses based on the design and performance of the framework. Some potential research questions are also suggested. Ultimately, this survey gives a clearer insight and can be used as a stepping stone to the research community in studying problems in this field.Comment: v1: 41 pages; v2: 40 page

Leveraging Decision Diagrams to Solve Two-stage Stochastic Programs with Binary Recourse and Logical Linking Constraints

Two-stage stochastic programs with binary recourse are challenging to solve and efficient solution methods for such problems have been limited. In this work, we generalize an existing binary decision diagram-based (BDD-based) approach of Lozano and Smith (Math. Program., 2018) to solve a special class of two-stage stochastic programs with binary recourse. In this setting, the first-stage decisions impact the second-stage constraints. Our modified problem extends the second-stage problem to a more general setting where logical expressions of the first-stage solutions enforce constraints in the second stage. We also propose a complementary problem and solution method which can be used for many of the same applications. In the complementary problem we have second-stage costs impacted by expressions of the first-stage decisions. In both settings, we convexify the second-stage problems using BDDs and parametrize either the arc costs or capacities of these BDDs with first-stage solutions depending on the problem. We further extend this work by incorporating conditional value-at-risk and we propose, to our knowledge, the first decomposition method for two-stage stochastic programs with binary recourse and a risk measure. We apply these methods to a novel stochastic dominating set problem and present numerical results to demonstrate the effectiveness of the proposed methods

Distributed learning automata-based scheme for classification using novel pursuit scheme

Author's accepted manuscript.Available from 03/03/2021.This is a post-peer-review, pre-copyedit version of an article published in Applied Intelligence. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10489-019-01627-w.acceptedVersio

Evolutionary games on graphs

Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first three sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fourth section surveys the topological complications implied by non-mean-field-type social network structures in general. The last three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.Comment: Review, final version, 133 pages, 65 figure