arXiv subjects

Partha Sarathi Mandal

Publications and source records attributed to Partha Sarathi Mandal.

35 records · Page 2Linked to original sources

arXiv2022

Approximation Algorithms for Drone Delivery Packing Problem

Recent advancements in unmanned aerial vehicles, also known as drones, have motivated logistics to use drones for multiple operations. Collaboration between drones and trucks in a last-mile delivery system has numerous benefits and reduces a number of challenges. In this paper, we introduce \textit{drone-delivery packing problem} (DDP), where we have a set of deliveries and respective customers with their prescribed locations, delivery time intervals, associated cost for deliveries, and a set of drones with identical battery budgets. The objective of the DDP is to find an assignment for all deliveries to the drones by using the minimum number of drones subject to the battery budget and compatibility of the assignment of each drone. We prove that DDP is NP-Hard and formulate the integer linear programming (ILP) formulation for it. We proposed two greedy approximation algorithms for DDP. The first algorithm uses at most $2OPT + (Δ+ 1)$ drones. The second algorithm uses at most $2OPT + ω$ drones, where OPT is the optimum solution for DDP, $ω$ is the maximum clique size, and $Δ$ is the maximum degree of the interval graph $G$ constructed from the delivery time intervals.

cs.DS↗

arXiv2022

Collaborative Dispersion by Silent Robots

In the dispersion problem, a set of $k$ co-located mobile robots must relocate themselves in distinct nodes of an unknown network. The network is modeled as an anonymous graph $G=(V,E)$, where the nodes of the graph are not labeled. The edges incident to a node $v$ with degree $d$ are labeled with port numbers in the range $0,1, \cdots, d-1$ at $v$. The robots have unique ids in the range $[0,L]$, where $L \ge k$, and are initially placed at a source node $s$. Each robot knows only its own id but does not know the ids of the other robots or the values of $L,k$. The task of dispersion was traditionally achieved with the assumption of two types of communication abilities: (a) when some robots are at the same node, they can communicate by exchanging messages between them (b) any two robots in the network can exchange messages between them. In this paper, we ask whether this ability of communication among co-located robots is necessary to achieve dispersion. We show that even if the ability of communication is not available, the task of dispersion by a set of mobile robots can be achieved in a much weaker model where a robot at a node $v$ has the access of following very restricted information at the beginning of any round: (1) am I alone at $v$? (2) the number of robots at $v$ increased or decreased compare to the previous round? We propose a deterministic algorithm that achieves dispersion on any given graph $G=(V,E)$ in time $O\left( k\log L+k^2 \log Δ\right)$, where $Δ$ is the maximum degree of a node in $G$. Each robot uses $O(\log L+ \log Δ)$ additional memory. We also prove that the task of dispersion cannot be achieved by a set of mobile robots with $o(\log L + \log Δ)$ additional memory.

cs.DS↗

arXiv2020

Fort Formation by an Automaton

Building structures by low capability robots is a very recent research development. A robot (or a mobile agent) is designed as a deterministic finite automaton. The objective is to make a structure from a given distribution of materials (\textit{bricks}) in an infinite grid $Z\times Z$. The grid cells may contain a brick (\textit{full cells}) or it may be empty (\textit{empty cells}). The \textit{field}, a sub-graph induced by the full cells, is initially connected. At a given point in time, a robot can carry at most one brick. The robot can move in four directions (north, east, south, and west) and starts from a \textit{full cell}. The \textit{Manhattan distance} between the farthest full cells is the \textit{span} of the field. We consider the construction of a \textit{fort}, a structure with the minimum span and maximum covered area. On a square grid, a fort is a hollow rectangle with bricks on the perimeter. We show that the construction of such a fort can be done in $O(z^2)$ time -- with a matching lower bound $Ω(z^2)$ -- where $z$ is the number of bricks present in the environment.

cs.CC↗

arXiv2020

A Distributed Algorithm for Overlapped Community Detection in Large-Scale Networks

Overlapped community detection in social networks has become an important research area with the increasing popularity and complexity of the networks. Most of the existing solutions are either centralized or parallel algorithms, which are computationally intensive - require complete knowledge of the entire networks. But it isn't easy to collect entire network data because the size of the actual networks may be prohibitively large. This may be a result of either privacy concerns or technological impediments. Performing in-network computation solves both problems utilizing the computational capability of the individual nodes of the network. Simultaneously, nodes communicate and share data with their neighbors via message passing, which may go a long way toward mitigating individual nodes' privacy concerns in the network. All the aforementioned concerns motivated us to design a decentralized or distributed technique to detect overlapped communities in a large-scale network. It is desirable because this technique does not offer a single point of failure, and the system as a whole can continue to function even when many of the nodes fail. In this paper, we address the overlapped community detection problem for large-scale networks. We present an efficient distributed algorithm, named DOCD, to identify the overlapped communities in the network. The DOCD algorithm's efficiency is verified with extensive simulation study on real network data such as Dolphin, Zachary karate club, Football club, and Facebook ego networks. We show that DOCD algorithm is capable of keeping the asymptotically same results with the existing classical centralized algorithms in terms of community modularity and the number of identified communities. The DOCD algorithm can also efficiently identify the overlapped nodes and overlapped communities with a small number of rounds of communication and computation.

cs.DC↗

arXiv2020

Conic Formation in Presence of Faulty Robots

Pattern formation is one of the most fundamental problems in distributed computing, which has recently received much attention. In this paper, we initiate the study of distributed pattern formation in situations when some robots can be \textit{faulty}. In particular, we consider the well-established \textit{look-compute-move} model with oblivious, anonymous robots. We first present lower bounds and show that any deterministic algorithm takes at least two rounds to form simple patterns in the presence of faulty robots. We then present distributed algorithms for our problem which match this bound, \textit{for conic sections}: in at most two rounds, robots form lines, circles and parabola tolerating $f=2,3$ and $4$ faults, respectively. For $f=5$, the target patterns are parabola, hyperbola and ellipse. We show that the resulting pattern includes the $f$ faulty robots in the pattern of $n$ robots, where $n \geq 2f+1$, and that $f < n < 2f+1$ robots cannot form such patterns. We conclude by discussing several relaxations and extensions.

cs.DC↗

arXiv2019

Randomized Gathering of Asynchronous Mobile Robots

This paper revisits the widely researched \textit{gathering} problem for two robots in a scenario which allows randomization in the asynchronous scheduling model. The scheduler is considered to be the adversary which determines the activation schedule of the robots. The adversary comes in two flavors, namely, oblivious and adaptive, based on the knowledge of the outcome of random bits. The robots follow \textit{wait-look-compute-move} cycle. In this paper, we classify the problems based on the capability of the adversary to control the parameters such as wait time, computation delay and the speed of robots and check the feasibility of gathering in terms of adversarial knowledge and capabilities. The main contributions include the possibility of gathering for an oblivious adversary with (i) zero computation delay; (ii) the sum of wait time and computation delay is more than a positive value. We complement the possibilities with an impossibility. We show that it is impossible for the robots to gather against an adaptive adversary with non-negative wait time and non-negative computation delay. Finally, we also extend our algorithm for multiple robots with merging.

cs.DC↗

arXiv2019

Chauffeuring a Crashed Robot from a Disk

Evacuation of robots from a disk has attained a lot of attention recently. We visit the problem from the perspective of fault-tolerance. We consider two robots trying to evacuate from a disk via a single hidden exit on the perimeter of the disk. The robots communicate wirelessly. The robots are susceptible to crash faults after which they stop moving and communicating. We design the algorithms for tolerating one fault. The objective is to minimize the worst-case time required to evacuate both the robots from the disk. When the non-faulty robot chauffeurs the crashed robot, it takes $α\geq 1$ amount of time to travel unit distance. With this, we also provide a lower bound for the evacuation time. Further, we evaluate the worst-case of the algorithms for different values of $α$ and the crash time.

cs.DC↗

arXiv2017

Evacuating Two Robots from Two Unknown Exits on the Perimeter of a Disk

Distributed evacuation of mobile robots is a recent development. We consider the evacuation problem of two robots which are initially located at the center of a unit disk. Both the robots have to evacuate the disk through the exits situated on the perimeter of the disk at an unknown location. The distance between two exits along the perimeter $d$ is given. We consider two different communication models. First, in the wireless model, the robots can send a message to each other over a long distance. Second, in face-to-face communication model, the robots can exchange information with each other only when they touch each other. The objective of the evacuation problem is to design an algorithm which minimizes the evacuation time of both the robots. For the wireless communication model, we propose a generic algorithm for two robots moving to two points on the perimeter with an initial separation of $ζ\leq d$. We also investigate evacuation problem for both unlabeled and labeled exits in the wireless communication model. For the face-to-face communication model, we propose two different algorithms for $ζ=0$ and $ζ=d$ for unlabeled exits. We also propose a generic algorithm for $ζ\leq d$ for labeled exits. We provide lower bounds corresponding to different $d$ values in the face-to-face communication model. We evaluate the performance our algorithms with simulation for both of the communication models.

cs.DC↗

arXiv2017

Approximation Algorithms for Barrier Sweep Coverage

Time-varying coverage, namely sweep coverage is a recent development in the area of wireless sensor networks, where a small number of mobile sensors sweep or monitor comparatively large number of locations periodically. In this article we study barrier sweep coverage with mobile sensors where the barrier is considered as a finite length continuous curve on a plane. The coverage at every point on the curve is time-variant. We propose an optimal solution for sweep coverage of a finite length continuous curve. Usually energy source of a mobile sensor is battery with limited power, so energy restricted sweep coverage is a challenging problem for long running applications. We propose an energy restricted sweep coverage problem where every mobile sensors must visit an energy source frequently to recharge or replace its battery. We propose a $\frac{13}{3}$-approximation algorithm for this problem. The proposed algorithm for multiple curves achieves the best possible approximation factor 2 for a special case. We propose a 5-approximation algorithm for the general problem. As an application of the barrier sweep coverage problem for a set of line segments, we formulate a data gathering problem. In this problem a set of mobile sensors is arbitrarily monitoring the line segments one for each. A set of data mules periodically collects the monitoring data from the set of mobile sensors. We prove that finding the minimum number of data mules to collect data periodically from every mobile sensor is NP-hard and propose a 3-approximation algorithm to solve it.

cs.DC↗

arXiv2016

Convergence of Even Simpler Robots without Location Information

The design of distributed gathering and convergence algorithms for tiny robots has recently received much attention. In particular, it has been shown that convergence problems can even be solved for very weak, \emph{oblivious} robots: robots which cannot maintain state from one round to the next. The oblivious robot model is hence attractive from a self-stabilization perspective, where state is subject to adversarial manipulation. However, to the best of our knowledge, all existing robot convergence protocols rely on the assumption that robots, despite being "weak", can measure distances. We in this paper initiate the study of convergence protocols for even simpler robots, called \emph{monoculus robots}: robots which cannot measure distances. In particular, we introduce two natural models which relax the assumptions on the robots' cognitive capabilities: (1) a Locality Detection ($\mathcal{LD}$) model in which a robot can only detect whether another robot is closer than a given constant distance or not, (2) an Orthogonal Line Agreement ($\mathcal{OLA}$) model in which robots only agree on a pair of orthogonal lines (say North-South and West-East, but without knowing which is which). The problem turns out to be non-trivial, and simple median and angle bisection strategies can easily increase the distances among robots (e.g., the area of the enclosing convex hull) over time. Our main contribution are deterministic self-stabilizing convergence algorithms for these two models, together with a complexity analysis. We also show that in some sense, the assumptions made in our models are minimal: by relaxing the assumptions on the \textit{monoculus robots} further, we run into impossibility results.

cs.DC↗

arXiv2016

Fault-Tolerant Gathering of Mobile Robots with Weak Multiplicity Detection

There has been a wide interest in designing distributed algorithms for tiny robots. In particular, it has been shown that the robots can complete certain tasks even in the presence of faulty robots. In this paper, we focus on gathering of all non-faulty robots at a single point in presence of faulty robots. We propose a wait-free algorithm (i.e., no robot waits for other robot and algorithm instructs each robot to move in every step, unless it is already at the gathering location), that gathers all non-faulty robots in semi-synchronous model without any agreement in the coordinate system and with weak multiplicity detection (i.e., a robot can only detect that either there is one or more robot at a location) in the presence of at most $n-1$ faulty robots for $n\geqslant 3$. We show that the required capability for gathering robots is minimal in the above model, since relaxing it further makes gathering impossible to solve. Also, we introduce an intermediate scheduling model \textit{ASYNC$_{IC}$} between the asynchronous ( i.e., no instantaneous movement or computation) and the semi-synchronous (i.e., both instantaneous movement and computation) as the asynchronous model with instantaneous computation. Then we propose another algorithm in \textit{ASYNC$_{IC}$} model for gathering all non-faulty robots with weak multiplicity detection without any agreement on the coordinate system in the presence of at most $\lfloor n/2\rfloor-2$ faulty robots for $n\geqslant 7$.

cs.DC↗

arXiv2014

Designing Path Planning Algorithms for Mobile Anchor towards Range-Free Localization

Localization is one of the most important factor in wireless sensor networks as many applications demand position information of sensors. Recently there is an increasing interest on the use of mobile anchors for localizing sensors. Most of the works available in the literature either looks into the aspect of reducing path length of mobile anchor or tries to increase localization accuracy. The challenge is to design a movement strategy for a mobile anchor that reduces path length while meeting the requirements of a good range-free localization technique. In this paper we propose two cost-effective movement strategies i.e., path planning for a mobile anchor so that localization can be done using the localization scheme \cite{Lee2009}. In one strategy we use a hexagonal movement pattern for the mobile anchor to localize all sensors inside a bounded rectangular region with lesser movement compared to the existing works in literature. In other strategy we consider a connected network in an unbounded region where the mobile anchor moves in the hexagonal pattern to localize the sensors. In this approach, we guarantee localization of all sensors within $r/2$ error-bound where $r$ is the communication range of the mobile anchor and sensors. Our simulation results support theoretical results along with localization accuracy.

cs.DC↗

arXiv2012

Optimal Covering with Mobile Sensors in an Unbounded Region

Covering a bounded region with minimum number of homogeneous sensor nodes is a NP-complete problem \cite{Li09}. In this paper we have proposed an {\it id} based distributed algorithm for optimal coverage in an unbounded region. The proposed algorithm guarantees maximum spreading in $O(\sqrt{n})$ rounds without creating any coverage hole. The algorithm executes in synchronous rounds without exchanging any message. We have also explained how our proposed algorithm can achieve optimal energy consumption and handle random sensor node deployment for optimal spreading.

cs.DC↗

arXiv2011

Fixing Data Anomalies with Prediction Based Algorithm in Wireless Sensor Networks

Data inconsistencies are present in the data collected over a large wireless sensor network (WSN), usually deployed for any kind of monitoring applications. Before passing this data to some WSN applications for decision making, it is necessary to ensure that the data received are clean and accurate. In this paper, we have used a statistical tool to examine the past data to fit in a highly sophisticated prediction model i.e., ARIMA for a given sensor node and with this, the model corrects the data using forecast value if any data anomaly exists there. Another scheme is also proposed for detecting data anomaly at sink among the aggregated data in the data are received from a particular sensor node. The effectiveness of our methods are validated by data collected over a real WSN application consisting of Crossbow IRIS Motes \cite{Crossbow:2009}.

cs.DC↗

arXiv2011

Secure Position Verification for Wireless Sensor Networks in Noisy Channels

Position verification in wireless sensor networks (WSNs) is quite tricky in presence of attackers (malicious sensor nodes), who try to break the verification protocol by reporting their incorrect positions (locations) during the verification stage. In the literature of WSNs, most of the existing methods of position verification have used trusted verifiers, which are in fact vulnerable to attacks by malicious nodes. They also depend on some distance estimation techniques, which are not accurate in noisy channels (mediums). In this article, we propose a secure position verification scheme for WSNs in noisy channels without relying on any trusted entities. Our verification scheme detects and filters out all malicious nodes from the network with very high probability.

cs.DC↗

arXiv2010

Reconstruction of Aggregation Tree in spite of Faulty Nodes in Wireless Sensor Networks

Recent advances in wireless sensor networks (WSNs) have led to many new promissing applications. However data communication between nodes consumes a large portion of the total energy of WSNs. Consequently efficient data aggregation technique can help greatly to reduce power consumption. Data aggregation has emerged as a basic approach in WSNs in order to reduce the number of transmissions of sensor nodes over {\it aggregation tree} and hence minimizing the overall power consumption in the network. If a sensor node fails during data aggregation then the aggregation tree is disconnected. Hence the WSNs rely on in-network aggregation for efficiency but a single faulty node can severely influence the outcome by contributing an arbitrary partial aggregate value. In this paper we have presented a distributed algorithm that reconstruct the aggregation tree from the initial aggregation tree excluding the faulty sensor node. This is a synchronous model that is completed in several rounds. Our proposed scheme can handle multiple number of faulty nodes as well.

cs.DC↗

arXiv2007

Deterministic Secure Positioning in Wireless Sensor Networks

Properly locating sensor nodes is an important building block for a large subset of wireless sensor networks (WSN) applications. As a result, the performance of the WSN degrades significantly when misbehaving nodes report false location and distance information in order to fake their actual location. In this paper we propose a general distributed deterministic protocol for accurate identification of faking sensors in a WSN. Our scheme does \emph{not} rely on a subset of \emph{trusted} nodes that are not allowed to misbehave and are known to every node in the network. Thus, any subset of nodes is allowed to try faking its position. As in previous approaches, our protocol is based on distance evaluation techniques developed for WSN. On the positive side, we show that when the received signal strength (RSS) technique is used, our protocol handles at most $\lfloor \frac{n}{2} \rfloor-2$ faking sensors. Also, when the time of flight (ToF) technique is used, our protocol manages at most $\lfloor \frac{n}{2} \rfloor - 3$ misbehaving sensors. On the negative side, we prove that no deterministic protocol can identify faking sensors if their number is $\lceil \frac{n}{2}\rceil -1$. Thus our scheme is almost optimal with respect to the number of faking sensors. We discuss application of our technique in the trusted sensor model. More precisely our results can be used to minimize the number of trusted sensors that are needed to defeat faking ones.

cs.CR↗