Related papers: A Novel Paradigm for Calculating Ramsey Number via…
A wide range of engineering design problems have been solved by the algorithms that simulates collective intelligence in swarms of birds or insects. The Artificial Bee Colony or ABC is one of the recent additions to the class of swarm…
Computer-based attempts to construct lower bounds for small Ramsey numbers are discussed. A systematic review of cyclic Ramsey graphs is attempted. Many known lower bounds are reproduced. Several new bounds are reported.
As an effective algorithm for solving complex optimization problems, artificial bee colony (ABC) algorithm has shown to be competitive, but the same as other population-based algorithms, it is poor at balancing the abilities of global…
Hyperparameter tuning in machine learning algorithms is a computationally challenging task due to the large-scale nature of the problem. In order to develop an efficient strategy for hyper-parameter tuning, one promising solution is to use…
In this paper we propose a network aware approach for routing in graded network using Artificial Bee Colony (ABC) algorithm. ABC has been used as a good search process for optimality exploitation and exploration. The paper shows how ABC…
Approximate Bayesian computation (ABC) methods perform inference on model-specific parameters of mechanistically motivated parametric statistical models when evaluating likelihoods is difficult. Central to the success of ABC methods is…
We describe here how the recent Wagner's approach for applying reinforcement learning to construct examples in graph theory can be used in the search for critical graphs for small Ramsey numbers. We illustrate this application by providing…
Ramsey theory is an active research area in combinatorics whose central theme is the emergence of order in large disordered structures, with Ramsey numbers marking the threshold at which this order first appears. For generalized Ramsey…
Artificial bee colony (ABC) algorithm has proved its importance in solving a number of problems including engineering optimization problems. ABC algorithm is one of the most popular and youngest member of the family of population based…
We prove new bounds for Ramsey numbers for book graphs $B_n$. In particular, we show that $R(B_{n-1},B_n) = 4n-1$ for an infinite family of $n$ using a block-circulant construction similar to Paley graphs. We obtain improved bounds for…
Block matching (BM) motion estimation plays a very important role in video coding. In a BM approach, image frames in a video sequence are divided into blocks. For each block in the current frame, the best matching block is identified inside…
The Ramsey number is the minimum number of nodes, $n = R(s, t)$, such that all undirected simple graphs of order $n$, contain a clique of order $s$, or an independent set of order $t$. This paper explores the application of a best first…
In this work, we give several new upper and lower bounds on Ramsey numbers for books and wheels, including a tight upper bound establishing $R(W_5, W_7) = 15$, matching upper and lower bounds giving $R(W_5, W_9) = 18$, $R(B_2, B_8) = 21$,…
To infer the parameters of mechanistic models with intractable likelihoods, techniques such as approximate Bayesian computation (ABC) are increasingly being adopted. One of the main disadvantages of ABC in practical situations, however, is…
Many recent statistical applications involve inference under complex models, where it is computationally prohibitive to calculate likelihoods but possible to simulate data. Approximate Bayesian Computation (ABC) is devoted to these complex…
A construction described by the current author in 2017 uses two linear `prototype' graphs to build a compound graph with Ramsey properties inherited from the prototypes. This paper describes a generalisation of that construction which has…
Memetic computation (MC) has emerged recently as a new paradigm of efficient algorithms for solving the hardest optimization problems. On the other hand, artificial bees colony (ABC) algorithms demonstrate good performances when solving…
Let $K\_{[k,t]}$ be the complete graph on $k$ vertices from which a set of edges, induced by a clique of order $t$, has been dropped. In this note we give two explicit upper bounds for $R(K\_{[k\_1,t\_1]},\dots, K\_{[k\_r,t\_r]})$ (the…
Ramsey's theorem, concerning the guarantee of certain monochromatic patterns in large enough edge-coloured complete graphs, is a fundamental result in combinatorial mathematics. In this work, we highlight the connection between this…
In this paper we introduce a general framework for proving lower bounds for various Ramsey type problems within random settings. The main idea is to view the problem from an algorithmic perspective: we aim at providing an algorithm that…