GraphReach: Position-Aware Graph Neural Network using Reachability Estimations

Majority of the existing graph neural networks(GNN) learn node embeddings that encode their local neighborhoods but not their positions. Consequently, two nodes that are vastly distant but located in similar local neighborhoods map to similar embeddings in those networks. This limitation prevents accurate performance in predictive tasks that rely on position information. In this paper, we develop GRAPHREACH , a position-aware inductive GNN that captures the global positions of nodes through reachability estimations with respect to a set of anchor nodes. The anchors are strategically selected so that reachability estimations across all the nodes are maximized. We show that this combinatorial anchor selection problem is NP-hard and, consequently, develop a greedy (1−1/e) approximation heuristic. Empirical evaluation against state-of-the-art GNN architectures reveal that GRAPHREACH provides up to 40% relative improvement in accuracy. In addition, it is more robust to adversarial attacks.

Performance of Algorithms using Domination Theory in Wireless Sensor Network with NS2

To prologue about a wireless sensor network let us understand network originally; how to connect host computers as well as communicate. Computers that are connected together are represented as topology, there are different types to name them star, bus, mesh, and grid. Researchers represented it as TCP i.e., transmission control protocol that has to be a wired connection through the network. As researcher worked, even without wired connection to the host computers could even be communicated through UDP called user datagram protocol. UDP gave nativity to the wireless sensor network, it has its own pros and cons. Now a day, there are a number of types of wireless sensor network like adhoc network, under water sensor network and vehicular sensor network. An organized design of routing protocol is available in wireless sensor network, and then Connected Dominating Set (CDS) is broadly used as a essential part as a backbone. To construct the Connected Dominating Set with its size as minimum, meta-heuristic, greedy, approximation, heuristic and distributed algorithmic approaches are predictable. These approaches are concentrated on deriving independent set and then constructing the Connected Dominating Set using Steiner tree, Unit Disk Graph and algorithms gives better result when graph has lesser number of nodes. For the networks that are generated in a fixed simulation area. A new approach is used for building Connected Dominating Set based on the concept of Edge Dominating Set

Theoretical Expectation versus Practical Performance of Jackson’s Heuristic

A basic 2-approximation heuristic was suggested by Jackson in early 50s last century for scheduling jobs with release times and due dates to minimize the maximum job lateness. The theoretical worst-case bound of 2 helps a little in practice, when the solution quality is important. The quality of the solution delivered by Jackson’s heuristic is closely related to the maximum job processing timepmax that occurs in a given problem instance and with the resultant interference with other jobs that such a long job may cause. We use the relationship ofpmaxwith the optimal objective value to obtain more accurate approximation ratio, which may drastically outperform the earlier known worst-case ratio of 2. This is proved, in practice, by our computational experiments.

Value-Function Approximations for Partially Observable Markov Decision Processes

Partially observable Markov decision processes (POMDPs) provide an elegant mathematical framework for modeling complex decision and planning problems in stochastic domains in which states of the system are observable only indirectly, via a set of imperfect or noisy observations. The modeling advantage of POMDPs, however, comes at a price -- exact methods for solving them are computationally very expensive and thus applicable in practice only to very simple problems. We focus on efficient approximation (heuristic) methods that attempt to alleviate the computational problem and trade off accuracy for speed. We have two objectives here. First, we survey various approximation methods, analyze their properties and relations and provide some new insights into their differences. Second, we present a number of new approximation methods and novel refinements of existing techniques. The theoretical results are supported by experiments on a problem from the agent navigation domain.