Search

The freeze tag problem (FTP) aims to awaken a swarm of robots with one or more initial awake robots as soon as possible. Each awake robot must touch a sleeping robot to wake it up. Once a robot is awakened, it can assist in awakening other sleeping robots. We study this problem inside a polygonal domain and present approximation algorithms for it., Comment: 7 pages, 3 figures

In the era of widespread social networks, the rapid dissemination of fake news has emerged as a significant threat, inflicting detrimental consequences across various dimensions of people's lives. Machine learning and deep learning approaches have been extensively employed for identifying fake news. However, a significant challenge in identifying fake news is the limited availability of labeled news datasets. Therefore, the One-Class Learning (OCL) approach, utilizing only a small set of labeled data from the interest class, can be a suitable approach to address this challenge. On the other hand, representing data as a graph enables access to diverse content and structural information, and label propagation methods on graphs can be effective in predicting node labels. In this paper, we adopt a graph-based model for data representation and introduce a semi-supervised and one-class approach for fake news detection, called LOSS-GAT. Initially, we employ a two-step label propagation algorithm, utilizing Graph Neural Networks (GNNs) as an initial classifier to categorize news into two groups: interest (fake) and non-interest (real). Subsequently, we enhance the graph structure using structural augmentation techniques. Ultimately, we predict the final labels for all unlabeled data using a GNN that induces randomness within the local neighborhood of nodes through the aggregation function. We evaluate our proposed method on five common datasets and compare the results against a set of baseline models, including both OCL and binary labeled models. The results demonstrate that LOSS-GAT achieves a notable improvement, surpassing 10%, with the advantage of utilizing only a limited set of labeled fake news. Noteworthy, LOSS-GAT even outperforms binary labeled models.

The protection of pathways holds immense significance across various domains, including urban planning, transportation, surveillance, and security. This article introduces a groundbreaking approach to safeguarding pathways by employing orthogonal robots. The study specifically addresses the challenge of efficiently guarding orthogonal areas with the minimum number of orthogonal robots. The primary focus is on orthogonal pathways, characterized by a path-like dual graph of vertical decomposition. It is demonstrated that determining the minimum number of orthogonal robots for pathways can be achieved in linear time. However, it is essential to note that the general problem of finding the minimum number of robots for simple polygons with general visibility, even in the orthogonal case, is known to be NP-hard. Emphasis is placed on the flexibility of placing robots anywhere within the polygon, whether on the boundary or in the interior., Comment: 8 pages, 5 figures

The Orthogonal Watchman Route Problem (OWRP) entails the search for the shortest path, known as the watchman route, that a robot must follow within a polygonal environment. The primary objective is to ensure that every point in the environment remains visible from at least one point on the route, allowing the robot to survey the entire area in a single, continuous sweep. This research places particular emphasis on reducing the number of turns in the route, as it is crucial for optimizing navigation in watchman routes within the field of robotics. The cost associated with changing direction is of significant importance, especially for specific types of robots. This paper introduces an efficient linear-time algorithm for solving the OWRP under the assumption that the environment is monotone. The findings of this study contribute to the progress of robotic systems by enabling the design of more streamlined patrol robots. These robots are capable of efficiently navigating complex environments while minimizing the number of turns. This advancement enhances their coverage and surveillance capabilities, making them highly effective in various real-world applications., Comment: 6 pages, 3 figures

Given two sets A={a_1,a_2,...,a_s} and {b_1,b_2,...,b_t}, a many-to-many matching with demands and capacities (MMDC) between A and B matches each element a_i in A to at least \alpha_i and at most \alpha'_i elements in B, and each element b_j in B to at least \beta_j and at most \beta'_j elements in A for all 1=

FAST problem is finding minimum feedback arc set problem in tournaments. In this paper we present some algorithms that are similar to sorting algorithms for FAST problem and we analyze them. We present Pseudo_InsertionSort algorithm for FAST problem and we show that average number of all backward edges in output of that is equal to ((n^2-5n+8)/4)-2^(1-n). We introduce Pseudo_MergeSort algorithm and we find the probability of being backward for an edge. Finally we introduce other algorithms for this problem., Comment: 9 pages, 15 figures

Given two point sets S and T, the minimum-cost many-to-many matching with demands (MMD) problem is the problem of finding a minimum-cost many-to-many matching between S and T such that each point of S (respectively T) is matched to at least a given number of the points of T (respectively S). We propose the first O(n^2) time algorithm for computing a one dimensional MMD (OMMD) of minimum cost between S and T, where |S|+|T|=n. In an OMMD problem, the input point sets S and T lie on the real line and the cost of matching a point to another point equals the distance between the two points. We also study a generalized version of the MMD problem, the many-to-many matching with demands and capacities (MMDC) problem, that in which each point has a limited capacity in addition to a demand. We give the first O(n^2) time algorithm for the minimum-cost one dimensional MMDC (OMMDC) problem., Comment: 15 pages,7 figures. arXiv admin note: substantial text overlap with arXiv:1702.01083

Given two sets S and T, a limited-capacity many-to-many matching (LCMM) between S and T matches each element p in S (resp. T) to at least 1 and at most Cap(p) elements in T (resp. S), where the function Cap:S\cup T-> Z>0 denotes the capacity of p. In this paper, we present the first linear time algorithm for finding a minimum-cost one-dimensional LCMM (OLCMM) between S and T, where S and T are points lying on a line, and the cost of matching p in S to q in T equals the l_2 distance between p,q. Our algorithm improves the previous best-known quadratic time algorithm., Comment: 31 pages, 8 figures. arXiv admin note: text overlap with arXiv:1702.01083

In complex networks, especially social networks, networks could be divided into disjoint partitions that the ratio between the number of internal edges (the edges between the vertices within same partition) to the number of outer edges (edges between two vertices of different partitions) is high. Generally, these partitions are called communities. Detecting these communities helps data scientists to extract meaningful information from graphs and analyze them. In the last decades, various algorithms have been proposed to detect communities in graphs, and each one has examined this issue from a different perspective. However, most of these algorithms have a significant time complexity and costly calculations that make them unsuitable to detect communities in large graphs with millions of edges and nodes. In this paper, we have tried to improve Label Propagation Algorithm by using edge betweenness metric, so that it is able to identify distinct communities in both real world and artificial networks in near linear time complexity with acceptable accuracy. Also, the proposed algorithm could detect communities in weighted graphs. Empirical experiments show that the accuracy and speed of the proposed algorithm are acceptable; additionally, the proposed algorithm is scalable., Comment: 29 pages, Extended Version

Given a simple polygon $ \mathcal {P} $ of $ n $ vertices in the Plane. We study the problem of computing the visibility area from a given viewpoint $ q $ inside $ \mathcal {P} $ where only sub-linear variables are allowed for working space. Without any memory-constrained, this problem was previously solved in $ O(n) $-time and $ O(n) $-variables space. In a newer research, the visibility area of a point be computed in $ O(n) $-time, using $ O(\sqrt{n}) $ variables for working space. In this paper, we present an optimal-time algorithm, using $ O(c/\log n) $ variables space for computing visibility area, where $ c

Classifiers trained using conventional empirical risk minimization or maximum likelihood methods are known to suffer dramatic performance degradations when tested over examples adversarially selected based on knowledge of the classifier's decision rule. Due to the prominence of Artificial Neural Networks (ANNs) as classifiers, their sensitivity to adversarial examples, as well as robust training schemes, have been recently the subject of intense investigation. In this paper, for the first time, the sensitivity of spiking neural networks (SNNs), or third-generation neural networks, to adversarial examples is studied. The study considers rate and time encoding, as well as rate and first-to-spike decoding. Furthermore, a robust training mechanism is proposed that is demonstrated to enhance the performance of SNNs under white-box attacks., Comment: Submitted for possible publication. arXiv admin note: text overlap with arXiv:1710.10704

Third-generation neural networks, or Spiking Neural Networks (SNNs), aim at harnessing the energy efficiency of spike-domain processing by building on computing elements that operate on, and exchange, spikes. In this paper, the problem of training a two-layer SNN is studied for the purpose of classification, under a Generalized Linear Model (GLM) probabilistic neural model that was previously considered within the computational neuroscience literature. Conventional classification rules for SNNs operate offline based on the number of output spikes at each output neuron. In contrast, a novel training method is proposed here for a first-to-spike decoding rule, whereby the SNN can perform an early classification decision once spike firing is detected at an output neuron. Numerical results bring insights into the optimal parameter selection for the GLM neuron and on the accuracy-complexity trade-off performance of conventional and first-to-spike decoding., Comment: A shorter version will be published on Proc. IEEE ICASSP 2018

Nowadays, identification and detection community structures in complex networks is an important factor in extracting useful information from networks. Label propagation algorithm with near linear-time complexity is one of the most popular methods for detecting community structures, yet its uncertainty and randomness is a defective factor. Merging LPA with other community detection metrics would improve its accuracy and reduce instability of LPA. Considering this point, in this paper we tried to use edge betweenness centrality to improve LPA performance. On the other hand, calculating edge betweenness centrality is expensive, so as an alternative metric, we try to use local edge betweenness and present LPA-LEB (Label Propagation Algorithm Local Edge Betweenness). Experimental results on both real-world and benchmark networks show that LPA-LEB possesses higher accuracy and stability than LPA when detecting community structures in networks., Comment: 6 pages

We are interested in the problem of guarding simple orthogonal polygons with the minimum number of $ r $-guards. The interior point $ p $ belongs an orthogonal polygon $ P $ is visible from $ r $-guard $ g $, if the minimum area rectangle contained $ p $ and $ q $ lies within $ P $. A set of point guards in polygon $ P $ is named guard set (as denoted $ G $) if the union of visibility areas of these point guards be equal to polygon $ P $ i.e. every point in $ P $ be visible from at least one point guards in $ G $. For an orthogonal polygon, if dual graph of vertical decomposition is a path, it is named path polygon. In this paper, we show that the problem of finding the minimum number of $ r $-guards (minimum guard set) becomes linear-time solvable in orthogonal path polygons. The path polygon may have dent edges in every four orientations. For this class of orthogonal polygon, the problem has been considered by Worman and Keil who described an algorithm running in $ O(n^{17} poly\log n) $-time where $ n $ is the size of the input polygon. The problem of finding minimum number of guards for simple polygon with general visibility is NP-hard, even if polygon be orthogonal. Our algorithm is purely geometric and presents a new strategy for $ r $-guarding orthogonal polygons and guards can be placed everywhere in the interior and boundary of polygon., Comment: arXiv admin note: substantial text overlap with arXiv:1708.05815

A hidden guard set $ G $ is a set of point guards in polygon $ P $ that all points of the polygon are visible from some guards in $ G $ under the constraint that no two guards may see each other. In this paper, we consider the problem for finding minimum hidden guard sets in histogram polygons under orthogonal visibility. Two points $ p $ and $ q $ are orthogonally visible if the orthogonal bounding rectangle for $ p $ and $ q $ lies within $ P $. It is known that the problem is NP-hard for simple polygon with general visibility and it is true for simple orthogonal polygon. We proposed a linear time exact algorithm for finding minimum hidden guard set in histogram polygons under orthogonal visibility. In our algorithm, it is allowed that guards place everywhere in the polygon.

Given an orthogonal polygon $ P $ with $ n $ vertices, the goal of the watchman route problem is finding a path $ S $ of the minimum length in $ P $ such that every point of the polygon $ P $ is visible from at least one of the point of $ S $. In the other words, in the watchman route problem we must compute a shortest watchman route inside a simple polygon of $ n $ vertices such that all the points interior to the polygon and on its boundary are visible to at least one point on the route. If route and polygon be orthogonal, it is called orthogonal watchman route problem. One of the targets of this problem is finding the orthogonal path with the minimum number of bends as possible. We present a linear-time algorithm for the orthogonal watchman route problem, in which the given polygon is monotone. Our algorithm can be used also for the problem on simple orthogonal polygons $ P $ for which the dual graph induced by the vertical decomposition of $ P $ is a path, which is called path polygon.

Given a graph $ G $ with $ n $ vertices and a set $ S $ of $ n $ points in the plane, a point-set embedding of $ G $ on $ S $ is a planar drawing such that each vertex of $ G $ is mapped to a distinct point of $ S $. A straight-line point-set embedding is a point-set embedding with no edge bends or curves. The point-set embeddability problem is NP-complete, even when $ G $ is $ 2 $-connected and $ 2 $-outerplanar. It has been solved polynomially only for a few classes of planar graphs. Suppose that $ S $ is the set of vertices of a simple polygon. A straight-line polygon embedding of a graph is a straight-line point-set embedding of the graph onto the vertices of the polygon with no crossing between edges of graph and the edges of polygon. In this paper, we present $ O(n) $-time algorithms for polygon embedding of path and cycle graphs in simple convex polygon and same time algorithms for polygon embedding of path and cycle graphs in a large type of simple polygons where $n$ is the number of vertices of the polygon.

Given two point sets S and T, we study the many-to-many matching with demands problem (MMD problem) which is a generalization of the many-to-many matching problem (MM problem). In an MMD, each point of one set must be matched to a given number of the points of the other set (each point has a demand). In this paper we consider a special case of MMD problem, the one-dimensional MMD (OMMD), where the input point sets S and T lie on the line. That is, the cost of matching a pair of points is equal to the distance between the two points. we present the first O(n^2)time algorithm for computing an OMMD between S and T, where |S| + |T| = n., Comment: 14 pages, 9 figures. arXiv admin note: text overlap with arXiv:1210.8123

Mobile cloud computing enables the offloading of computationally heavy applications, such as for gaming, object recognition or video processing, from mobile users (MUs) to cloudlet or cloud servers, which are connected to wireless access points, either directly or through finite-capacity backhaul links. In this paper, the design of a mobile cloud computing system is investigated by proposing the joint optimization of computing and communication resources with the aim of minimizing the energy required for offloading across all MUs under latency constraints at the application layer. The proposed design accounts for multiantenna uplink and downlink interfering transmissions, with or without cooperation on the downlink, along with the allocation of backhaul and computational resources and user selection. The resulting design optimization problems are nonconvex, and stationary solutions are computed by means of successive convex approximation (SCA) techniques. Numerical results illustrate the advantages in terms of energy-latency trade-off of the joint optimization of computing and communication resources, as well as the impact of system parameters, such as backhaul capacity, and of the network architecture., Comment: 15 pages, 10 figures. To appear on IEEE Transactions on Signal and Information Processing over Networks

We study the Hamiltonian path problem in C-shaped grid graphs, and present the necessary and sufficient conditions for the existence of a Hamiltonian path between two given vertices in these graphs. We also give a linear-time algorithm for finding a Hamiltonian path between two given vertices of a C-shaped grid graph, if it exists., Comment: 28 pages, 31 figures, and 20 references

In this paper the design for an absorbing metamaterial with near unity absorbance in terahertz region is presented. The absorber's unit cell structure consists of two metamaterial resonators that couple to electric and magnetic fields separately. The structure allows us to maximize absorption by varying dielectric material and thickness and, hence the effective electrical permittivity and magnetic permeability.

Although, the Hamiltonicity of solid grid graphs are polynomial-time decidable, the complexity of the longest cycle problem in these graphs is still open. In this paper, by presenting a linear-time constant-factor approximation algorithm, we show that the longest cycle problem in solid grid graphs is in APX. More precisely, our algorithm finds a cycle of length at least $\frac{2n}{3}+1$ in 2-connected $n$-node solid grid graphs. Keywords: Longest cycle, Hamiltonian cycle, Approximation algorithm, Solid grid graph., Comment: 11 pages, 6 figures