A Random Walk Perspective on Hide-and-Seek Games

We investigate hide-and-seek games on complex networks using a random walk framework. Specifically, we investigate the efficiency of various degree-biased random walk search strategies to locate items that are randomly hidden on a subset of vertices of a random graph. Vertices at which items are hidden in the network are chosen at random as well, though with probabilities that may depend on degree. We pitch various hide and seek strategies against each other, and determine the efficiency of search strategies by computing the average number of hidden items that a searcher will uncover in a random walk of $n$ steps. Our analysis is based on the cavity method for finite single instances of the problem, and generalises previous work of De Bacco et al. [1] so as to cover degree-biased random walks. We also extend the analysis to deal with the thermodynamic limit of infinite system size. We study a broad spectrum of functional forms for the degree bias of both the hiding and the search strategy and investigate the efficiency of families of search strategies for cases where their functional form is either matched or unmatched to that of the hiding strategy. Our results are in excellent agreement with those of numerical simulations. We propose two simple approximations for predicting efficient search strategies. One is based on an equilibrium analysis of the random walk search strategy. While not exact, it produces correct orders of magnitude for parameters characterising optimal search strategies. The second exploits the existence of an effective drift in random walks on networks, and is expected to be efficient in systems with low concentration of small degree nodes.Comment: 31 pages, 10 (multi-part) figure

Approximation algorithms for Capacitated Facility Location Problem with Penalties

In this paper, we address the problem of capacitated facility location problem with penalties (CapFLPP) paid per unit of unserved demand. In case of uncapacitated FLP with penalties demands of a client are either entirely met or are entirely rejected and penalty is paid. In the uncapacitated case, there is no reason to serve a client partially. Whereas, in case of CapFLPP, it may be beneficial to serve a client partially instead of not serving at all and, pay the penalty for the unmet demand. Charikar et. al. \cite{charikar2001algorithms}, Jain et. al. \cite{jain2003greedy} and Xu- Xu \cite{xu2009improved} gave $3$, $2$ and $1.8526$ approximation, respectively, for the uncapacitated case . We present $(5.83 + \epsilon)$ factor for the case of uniform capacities and $(8.532 + \epsilon)$ factor for non-uniform capacities

Implementation Paper Modern and Smart Logistic Vehicle Using Tracking and Security

The logistic organization structure have climbed beginning late with the improvement of global positioning system (GPS), helpful correspondence movements, sensor and remote structures association advancements. The collaborations of the administrators system are fundamental as they can add to a few points of enthusiasm, for example, proposing right places for getting clients, developing pay of truck drivers, reducing holding up time, vehicle downpours and besides compelling fuel utilization and from this time forward broadening the measure of treks the drivers can perform. The rule motivation driving this structure would supply required vehicles that would be utilized to meet client requests through the arranging, control and utilization of the noteworthy headway and cutoff of related data and associations from beginning to objective. Customer brings to the table start to finish security to client and supplier information by utilizing QR code thought. Customer is proposition of closest best specialist relationship as shown by client intrigue and recognize spam master network. Joint efforts association suggests the commitment and association of plan and direct structures to control the improvement and land masterminding of foul materials, work-in-process, and completed inventories at the most unimportant all out expense. Composed endeavours solidifies the relationship of enthusiasm organizing, stock, transportation, and the mix of warehousing, materials managing, and packaging, all joined all through an arrangement of workplaces