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The 9th International Conference on Mathematics and computing (ICMC 2023)

作者： Koley, Subhasis Ghosh, Sasthi C. Advanced Computing and Microelectronics unit Indian Statistical Institute 203 B. T. Road Kolkata700108 India

ISBN: (纸本)9789819930791

Let us take two given integers h and k where h, k≥ 0 and a graph G= (V(G), E(G) ). An L(h, k)-edge-labeling for G is defined as a function f′: E(G) → { 0, 1, ⋯, n} such that ∀ e1, e2∈ E(G), | f′(e1) - f′(e2) | ≥ h when d′(e1, e2) = 1 and | f′(e1) - f′(e2) | ≥ k when d′(e1, e2) = 2 where d′(e1, e2) denotes the distance between e1 and e2 in G. If there is no other way to connect e1 and e2 with less than k′- 1 number of edges in G, then d′(e1, e2) = k′. The objective is to find the span which is the least value of n obtained over all such L(h, k)-edge-labeling for G, and it is denoted as λh,k′(G). Motivated from the channel assignment problem in wireless network, L(h, k)-edge-labeling has been studied for various infinite regular grid graphs. For infinite 8-regular grid T8, it is known in the existing literature that 25≤λ1,2′(T8)≤28. But the lower and upper bounds obtained there are not identical. Here, we improve the lower bound and prove that λ1,2′(T8)≥28 and eventually it is proved that λ1,2′(T8)=28. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd 2023.

关键词： Combinatorial optimization

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Anomaly Detection in Evolutionary Social Networks leveraging Community Structure 15

Anomaly Detection in Evolutionary Social Networks leveraging...

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15th IEEE International Conference on Service Operations and Logistics, and Informatics, SOLI 2021

作者： Ghoshal, Arnab Kumar Das, Nabanita Asutosh College Department of Computer Science Kolkata India Advanced Computing and Microelectronics Unit Indian Statistical Institute Kolkata India

ISBN: (纸本)9781665467223

Social networks are temporally evolving by nature and in general, the evolution takes place gradually with time. But occasionally, the nodes may exhibit anomalous behavior that is to be detected and reported in real time. Usually, the social networks are represented as a temporal stream of weighted graphs, where edge weights stand for frequency or power of actions. Here, for identification of anomalies in evolutionary social networks, we follow an action based approach leveraging the community structure of the network, where it is shown that only the Community Boundary Nodes are enough to detect anomaly in a temporally evolving social network. We introduce a new definition of anomaly score for nodes based on its action history. To the best of our knowledge, this is the first work to exploit the community boundary nodes of an evolutionary social network to identify the graph snapshots containing anomalous events. Experimental studies on real-world as well as synthetic evolutionary networks show that the proposed technique achieves almost 13% improvement in F-Score compared to the state-of-the-art algorithms. Moreover, parallel implementation of the proposed technique results nearly 6 x speedup making it suitable for real time computation of anomaly in evolutionary social networks. © 2021 IEEE.

关键词： Anomaly detection

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Minimum enclosing circle of a set of fixed points and a mobile point

Minimum enclosing circle of a set of fixed points and a mobi...

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作者： Banik, Aritra Bhattacharya, Bhaswar B. Das, Sandip Advanced Computing and Microelectronics Unit Indian Statistical Institute Kolkata India Department of Statistics Stanford University CA United States

Given a set S of n static points and a mobile point p in R2, we study the variations of the smallest circle that encloses S{p} when p moves along a straight line . In this work, a complete characterization of the locus of the center of the minimum enclosing circle (MEC) of S{p}, for p, is presented. The locus is a continuous and piecewise differentiable linear function, and each of its differentiable pieces lies either on the edges of the farthest-point Voronoi diagram of S, or on a line segment parallel to the line . Moreover, the locus has O(n) differentiable pieces, which can be computed in linear time, given the farthest-point Voronoi diagram of S. © 2014 Elsevier B.V.

关键词： Computational geometry

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Proving a Conjecture on 8-Distance Coloring of the Infinite Hexagonal Grid? 22

Proving a Conjecture on 8-Distance Coloring of the Infinite ...

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22nd Italian Conference on Theoretical Computer Science, ICTCS 2021

作者： Ghosh, Sasthi C. Koley, Subhasis Advanced Computing And Microelectronics Unit Indian Statistical Institute 203 B. T. Road Kolkata700108 India

Given p ∈ N, a p distance coloring is a coloring f : V → {1, 2, · · · , n} of the vertices of G such that f(u) 6= f(v) for all pair of vertices u and v in G where d(u, v), the distance between u and v, is at most p. Here d(u, v) is defined as the minimum number of edges required to connect u and v in G. The p distance chromatic number λ p (G) of a graph G is the minimum n such that G admits a p distance coloring of G. Such type of distance coloring is relevant when frequency assignment problem is formulated as a graph coloring problem. In the context of frequency assignment problem, sometimes cellular network can be modelled as an infinite hexagonal grid TH. Therefore λ p (TH) has practical relevance. For even p ≥ 8, it was conjectured by Jacko and Jendrol [Discussiones Mathematicae Graph Theory, 2005] that λ p (TH) = " 3 8 p + 4 3 2 # where [x] is an integer, x ∈ R and x - 1 2 © 2021 CEUR-WS. All rights reserved.

关键词： Coloring

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A Geometry-Based Strategic Placement of RISs in Millimeter Wave Device to Device Communication 3rd

A Geometry-Based Strategic Placement of RISs in Millimeter...

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3rd International Conference on Computer and Communication Engineering, CCCE 2023

作者： Sau, Lakshmikanta Ghosh, Sasthi C. Advanced Computing and Microelectronics Unit Indian Statistical Institute 203 B. T. Road Kolkata700108 India

ISBN: (纸本)9783031352980

Recently, reconfigurable intelligent surfaces (RISs) have been introduced in millimeter wave (mmWave) device to device (D2D) communication scenarios to provide seamless connection and high data rate to a pair of proximity users. However, such high data rate can be achieved, only if the concerned device pair resides in close proximity and a direct line of sight (LoS) link exists between them. The proximity and the LoS link is necessary because of the high propagation and penetration losses of the mmWaves. The direct LoS link between a pair of devices may be blocked easily by static obstacles like buildings and trees. If there is no such direct LoS link between a pair of devices, we can use RIS to form an indirect LoS link between them. However, in that case, proper placement of RISs is necessary to provide such indirect LoS link. In this work, we develop a RIS placement strategy to serve those device pairs who do not have any direct LoS links. In order to provide an indirect LoS link for a requesting device pair, we first use some basic ideas from computational geometry to find out the candidate zones for placing RISs. Next we find the candidate zones for all such requesting device pairs considering the fact that two or more candidate zones may overlap and create a new candidate zone. We construct a graph where each candidate zone represents a vertex and there exist an edge between two overlapping candidate zones. We convert the RIS placement problem to a clique partitioning problem of the graph and use a greedy algorithm to get a near optimal solution. From simulation results, we can see that the strategically placed RISs give better performance in comparison to an existing deployment strategy, which places RISs only on the walls of the building. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Millimeter waves

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Mobility Aware Path Selection for Millimeterwave 5G Networks in the Presence of Obstacles 3rd

Mobility Aware Path Selection for Millimeterwave 5G Network...

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3rd International Conference on Computer and Communication Engineering, CCCE 2023

作者： Sarkar, Subhojit Ghosh, Sasthi C. Advanced Computing and Microelectronics Unit Indian Statistical Institute 203 B. T. Road Kolkata700108 India

ISBN: (纸本)9783031352980

An often overlooked metric in millimeterwave communication is the so-called stability of assigned links. Links can fail due to obstacles (both static and dynamic), and user mobility. Handling static obstacles is easy;the challenge comes in tracking dynamic obstacles which may impede transmission in the near future. Most works in literature track dynamic obstacles by using additionally deployed hardware like radars and cameras, which add to deployment cost. Our approach requires no such additional hardware. We handle multiple static obstacles, and a single dynamic obstacle, to allocate stable transmission paths which are unlikely to break in the near future. We then adopt a holistic approach to the problem of transmission path allocation, by assigning paths that are estimated to be active for the longest possible time, albeit at the cost of some individual throughput. In other words, we do not always select the best link based on instantaneous system parameters;rather, we can counter-intuitively choose slower, but more stable links. To achieve this, we consider user mobility, and obstacles which may cause links to fail prematurely. We demonstrate the accuracy with which dynamic obstacle trajectories can be captured by our proposed approach. By further simulation studies, we show that our approach leads to the assignment of more stable links as compared to the traditional received signal strength based greedy approach. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： 5G mobile communication systems

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Gracefulness of vertex duplicated complete bipartite graph for static and incremental frequency allocation

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Electronic Notes in Discrete Mathematics 2015年 48卷 89-93页

作者： Sandhupatla, Amruth Ghosh, Sasthi C. Department of Electronics and Communication Engineering National Institute of Technology Warangal India Advanced Computing and Microelectronics Unit Indian Statistical Institute Kolkata India

We consider the vertex duplicated complete bipartite graph G'(VA, VB) which is formed by duplicating all the vertices of a complete bipartite graph G(A, B). We then deal with the gracefulness of G'(VA, VB) by ... 详细信息

We consider the vertex duplicated complete bipartite graph G^'(V_A, V_B) which is formed by duplicating all the vertices of a complete bipartite graph G(A, B). We then deal with the gracefulness of G^'(V_A, V_B) by considering both static and incremental frequency allocation to it. We have proved that the graceful labeling of G^'(V_A, V_B) is possible only for the case of static frequency allocation but not for the incremental frequency allocation. Finally we have shown that graceful labeling of G(A, B) satisfying certain additional properties can be extended to a σ-labeling of G^'(V_A, V_B) for the incremental frequency allocation. © 2015 Elsevier B.V.

关键词： Complete bipartite graph Frequency allocation Graceful labeling

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Chronological Orderings of Interval Digraph

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Electronic Notes in Discrete Mathematics 2003年 15.0卷 182-185页

作者： Talukdar, Malay Sen P. Das, Sandip Department of Mathematics University of North Bengal Darjeeling West Bengal India Advanced Computing and Microelectronics Unit Indian Statistical Institute Kolkata India

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Estimating checkpointing, rollback and recovery overheads

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5th International Workshop on Distributed computing, IWDC 2003

作者： Mandal, Partha Sarathi Mukhopadhyaya, Krishnendu Advanced Computing and Microelectronics Unit Indian Statistical Institute 203 B T Road Kolkata700108 India

ISBN: (纸本)3540207457

There are several schemes for checkpointing and rollback recovery. In this paper, we analyze some such schemes under a stochastic model. We have found expressions for average cost of checkpointing, rollback recovery, message logging and piggybacking with application messages in synchronous as well as asynchronous checkpointing. For quasi-synchronous checkpointing we show that in a system with n processes, the upper bound and lower bound of selective message logging are O(n2) and O(n) respectively. © Springer-Verlag Berlin Heidelberg 2003.

关键词： Stochastic models

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Approximation algorithms for deployment of sensors for line segment coverage in wireless sensor networks

Approximation algorithms for deployment of sensors for line ...

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2012 4th International Conference on Communication Systems and Networks, COMSNETS 2012

作者： Dash, Dinesh Bishnu, Arijit Gupta, Arobinda Nandy, Subhas C. Department of Computer Science and Engineering Indian Institute of Technology Kharagpur India Advanced Computing and Microelectronics Unit Indian Statistical Institute India

ISBN: (纸本)9781467302982

The coverage problem in wireless sensor network deals with the problem of covering a region or parts of it with sensors. In this paper, we address the problem of covering a set of line segments with minimum number of sensors. A line segment is said to be 1-covered if it intersects the sensing region of at least one among the sensors distributed in a bounded rectangular region R. We assume that the sensing radius of each sensor is uniform. The problem of finding the minimum number of sensors needed to 1-cover each member in a given set of line segments in R is NP-hard. We propose two constant factor approximation algorithms and a PTAS (Polynomial Time Approximation Scheme) for the problem for 1-covering a set of axis-parallel line segments. We also show that a PTAS exists for 1-covering a set of arbitrarily oriented line segments in R where the length of the line segments are bounded within a constant factor of the sensing radius of each sensor. © 2012 IEEE.

关键词： Wireless sensor networks

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