Krishnendu Mukhopadhyaya | Indian Statistical Institute, Calcutta (original) (raw)

Papers by Krishnendu Mukhopadhyaya

Journal of Parallel and Distributed Computing, 2006

Several schemes for checkpointing and rollback recovery have been reported in the literature. In ... more Several schemes for checkpointing and rollback recovery have been reported in the literature. In this paper, we analyze some of these schemes under a stochastic model. We have derived 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(n 2) and O(n), respectively.

Springer eBooks, 2005

If the variables used for the checkpointing algorithm have data faults, the algorithm may fail. I... more If the variables used for the checkpointing algorithm have data faults, the algorithm may fail. In this paper, a self- stabilizing checkpointing algorithm is proposed for handling data faults in a ring network. The proposed algorithm can deal with concurrent initiation of checkpointing and at most one data fault per process. However, several processes may be faulty.

Journal of Parallel and Distributed Computing, Jul 1, 2007

If the variables used for a checkpointing algorithm have data faults, the existing checkpointing ... more If the variables used for a checkpointing algorithm have data faults, the existing checkpointing and recovery algorithms may fail. In this paper, self-stabilizing data fault detecting and correcting, checkpointing, and recovery algorithms are proposed in a ring topology. The proposed data fault detection and correction algorithms can handle data faults; at most one per process, but in any number of processes. The proposed checkpointing algorithm can deal with concurrent multiple initiations of checkpointing and data faults. A process can recover from a fault, using the proposed recovery algorithm in spite of multiple data faults present in the system. All the proposed algorithms converge in O(n) steps, where n is the number of processes. The algorithm can be extended to work for general topologies too.

Proceedings of the 23rd International Conference on Distributed Computing and Networking, 2022

The gathering over meeting nodes problem requires the mobile robots to gather at one of the pre-d... more The gathering over meeting nodes problem requires the mobile robots to gather at one of the pre-defined meeting nodes. The robots are deployed on the nodes of an anonymous two-dimensional infinite grid which has a subset of nodes marked as meeting nodes. This work addresses the solvability of the problem under different settings. The problem has been studied under the objective function that minimizes the total number of moves made by all the robots to finalize the gathering task. A variation of the problem considers two disjoint and finite groups of anonymous robots. The problem also comprises two finite and disjoint sets of heterogeneous meeting nodes. Each robot in the first (resp. second) group must gather at one of the meeting nodes belonging to the first (resp. second) set.

arXiv (Cornell University), Aug 9, 2017

This paper addresses the mutual visibility problem for a set of semi-synchronous, opaque robots o... more This paper addresses the mutual visibility problem for a set of semi-synchronous, opaque robots occupying distinct positions in the Euclidean plane. Since robots are opaque, if three robots lie on a line, the middle robot obstructs the visions of the two other robots. The mutual visibility problem asks the robots to coordinate their movements to form a configuration, within finite time and without collision, in which no three robots are collinear. Robots are endowed with a constant bits of persistent memory. In this work, we consider the FSTATE computational model in which the persistent memory is used by the robots only to remember their previous internal states. Except from this persistent memory, robots are oblivious i.e., they do not carry forward any other information from their previous computational cycles. The paper presents a distributed algorithm to solve the mutual visibility problem for a set of semi-synchronous robots using only 1 bit of persistent memory. The proposed algorithm does not impose any other restriction on the capability of the robots and guarantees collision-free movements for the robots.

Journal of Parallel and Distributed Computing

In the existing literature of the MUTUAL VISIBILITY problem for autonomous robot swarms, the adop... more In the existing literature of the MUTUAL VISIBILITY problem for autonomous robot swarms, the adopted visibility models have some idealistic assumptions that are not consistent with practical sensing device implementations. This paper investigates the problem in the more realistic visibility model called opaque fat robots with slim omnidirectional camera. The robots are modeled as unit disks, each having an omnidirectional camera represented as a disk of smaller size. We assume that the robots have compasses that allow agreement in the direction and orientation of both axes of their local coordinate systems. The robots are equipped with visible lights which serve as a medium of communication and also as a form of memory. We present a distributed algorithm for the MUTUAL VISIBILITY problem which is provably correct in the semi-synchronous setting. Our algorithm also provides a solution for LEADER ELECTION which we use as a subroutine in our main algorithm. Although LEADER ELECTION is trivial with two axis agreement in the full visibility model, it is challenging in our case and is of independent interest.

ArXiv, 2020

In this paper, we study the circle formation problem by multiple autonomous and homogeneous disc-... more In this paper, we study the circle formation problem by multiple autonomous and homogeneous disc-shaped robots (also known as fat robots). The goal of the robots is to place themselves on the periphery of a circle. Circle formation has many real-world applications, such as boundary surveillance. This paper addresses one variant of such problem { uniform circle formation, where the robots have to be equidistant apart. The robots operate by executing cycles of the states wait-look-compute-move. They are oblivious, indistinguishable, anonymous, and do not communicate via message passing. First, we solve the uniform circle formation problem while assuming the robots to be transparent. Next, we address an even weaker model, where the robots are non-transparent and have limited visibility. We propose novel distributed algorithms to solve these variants. Our presented algorithms in this paper are proved to be correct and guarantee to prevent collision and deadlock among the swarm of robots.

23rd International Conference on Distributed Computing and Networking, 2022

A solution to the k-circle formation problem requires the formation of disjoint circles by a swar... more A solution to the k-circle formation problem requires the formation of disjoint circles by a swarm of mobile robots. The circles are restricted to be centered at one of the pre-fixed points. Each circle must contain exactly k robots at distinct positions. The robots are oblivious, autonomous, anonymous, homogeneous, and silent. They operate in Look-Compute-Move cycles under a fair asynchronous scheduler. This study addresses the solvability of the k-circle formation in the Euclidean plane. The k-circle formation is studied for point robots under one axis agreement. The relationship between the k-circle formation and the k-EPF (A generalized embedded pattern formation) problem is also studied. The solvability of the k-circle formation is investigated for disoriented point robots. Finally, the problem is considered for fat robots under one axis agreement.

ArXiv, 2015

Localization is an important issue for Wireless Sensor Networks (WSN). A mobile sensor may change... more Localization is an important issue for Wireless Sensor Networks (WSN). A mobile sensor may change its position rapidly and thus require localization calls frequently. A localization may require network wide information and increase traffic over the network. It dissipates valuable energy for message communication. Thus localization is very costly. The control of the number of localization calls may save energy consumption, as it is rather expensive. To reduce the frequency of localization calls for a mobile sensor, we propose a technique that involves \textit{Mobility Aware Interpolation} (MAINT) for position estimation. It controls the number of localizations which gives much better result than the existing localization control schemes using mobility aware extrapolation. The proposed method involves very low arithmetic computation overheads. We find analytical expressions for the expected error in position estimation. A parameter, the time interval, has been introduced to externally...

Structural Information and Communication Complexity, 2019

This paper presents a study of the mutual visibility problem for a set of opaque asynchronous rob... more This paper presents a study of the mutual visibility problem for a set of opaque asynchronous robots in the Euclidean plane. Due to opacity, if three robots lie on a line, the middle robot obstructs the visions of the two other robots. The mutual visibility problem requires the robots to coordinate their movements to form a configuration in which no three robots are collinear. This work presents a distributed algorithm which solves the mutual visibility problem for a set of \(n\ge 2\) asynchronous robots under the FState computational model. The proposed algorithm assumes 1 bit of persistent memory and the knowledge of n. The proposed solution works under the non-rigid movements of the robots and also provides collision free movements for the robots.

Algorithms and Discrete Applied Mathematics, 2020

The gathering over meeting nodes problem asks the robots to gather at one of the pre-defined meet... more The gathering over meeting nodes problem asks the robots to gather at one of the pre-defined meeting nodes. The robots are deployed on the nodes of an anonymous two-dimensional infinite grid which has a subset of nodes marked as meeting nodes. Robots are identical, autonomous, anonymous and oblivious. They operate under an asynchronous scheduler. They do not have any agreement on a global coordinate system. All the initial configurations for which the problem is deterministically unsolvable have been characterized. A deterministic distributed algorithm has been proposed to solve the problem for the remaining configurations. The efficiency of the proposed algorithm is studied in terms of the number of moves required for gathering. A lower bound concerning the total number of moves required to solve the gathering problem has been derived.

This work addresses the problem of Gathering a swarm of point robots when the plane of deployment... more This work addresses the problem of Gathering a swarm of point robots when the plane of deployment has non-intersecting transparent convex polygonal obstacles. While multiplicity detection is enough for gathering three or more asynchronous robots without obstacles, it is shown that in the presence of obstacles, gathering may not be possible even in the FSYNC model with all of multiplicity detection, memory, chirality and direction-only axis agreement. Initial configurations for which gathering is impossible are characterized. For other configurations, a distributed algorithm for the gathering problem is proposed without any extra assumption on the capabilities of the robots. The algorithm works even if the configuration contains points of multiplicities.

Distributed Computing by Mobile Entities, 2019

In a swarm of robots, each robot has certain capabilities to perform their computations to achiev... more In a swarm of robots, each robot has certain capabilities to perform their computations to achieve a global objective. One such capability is the sensing capability, known as vision. This enables a robot to sense the positions of the other robots in the system. The sensing capability may be restricted by two factors: (i) the sensing range and (ii) the opacity of the robots. The sensing range may be limited or unlimited and the robots may be transparent or opaque. When robots have limited sensing range, a robot can sense all the robots within a fixed radius around it. If three opaque robots are collinear, the middle robot obstructs the vision of the two other robots. This chapter deals with these two constraints on the vision of the robots. A model with such a constraint is referred to as the restricted visibility model. This chapter presents different geometric formation problems for swarm robots under the restricted visibility model.

Handbook of Research on Design, Control, and Modeling of Swarm Robotics

A swarm of robots is a collection of tiny identical autonomous robots. The robots perform a given... more A swarm of robots is a collection of tiny identical autonomous robots. The robots perform a given task, e.g., cleaning a big surface, moving a big object, guarding an area etc., in a collaborative framework. The goal of research in swarm robotics is to develop a low cost multi-robot system which will be at least as efficient as one big expensive unit. The field of swarm robotics has been addressed from various aspects such as artificial intelligence, mechanical and electrical engineering, motion control, robots' path planning etc. From theoretical point of view, designing deterministic algorithms for these robots to execute a particular job is an emerging and useful field of research. As the robots work individually but in collaboration, distributed algorithms are more appropriate than centralized ones. This chapter discusses the distributed framework for swarm robots and presents some reported research results as well as a few open problems.

Theoretical Computer Science, 2022

ArXiv, 2022

The gathering over meeting nodes problem requires the robots to gather at one of the predefined m... more The gathering over meeting nodes problem requires the robots to gather at one of the predefined meeting nodes. This paper investigates the problem with respect to the objective function that minimizes the total number of moves made by all the robots. In other words, the sum of the distances traveled by all the robots is minimized while accomplishing the gathering task. The robots are deployed on the nodes of an anonymous two-dimensional infinite grid which has a subset of nodes marked as meeting nodes. The robots do not agree on a global coordinate system and operate under an asynchronous scheduler. A deterministic distributed algorithm has been proposed to solve the problem for all those solvable configurations, and the initial configurations for which the problem is unsolvable have been characterized. The proposed gathering algorithm is optimal with respect to the total number of moves performed by all the robots in order to finalize the gathering.

ArXiv, 2014

AbstractThis paper presents a deterministic algorithm for forming a given asymmetricpattern in ni... more AbstractThis paper presents a deterministic algorithm for forming a given asymmetricpattern in nite time by a set of autonomous, homogeneous, oblivious mobilerobots under the CORDA model. The robots are represented as points on the2D plane. There is no explicit communication between the robots. The robotscoordinate among themselves by observing the positions of the other robots onthe plane. Initially all the robots are assumed to be stationary. The robotshave local coordinate systems de ned by Sense of Direction (SoD), orientationor chirality and scale. Initially the robots are in asymmetric con guration. Weshow that these robots can form any given asymmetric pattern in nite time.Keywords: Asynchronous, oblivious, mobile robots, pattern formation,chirality.1. IntroductionExecuting a collaborative task by a set of small, autonomous, mobile robots(also known as robot swarm [18]) has been a popular topic for the researchfor last few decades. The robots are assumed to be anonymous, homo...

This paper considers a constrained version of the circle formation problem for a set of asynchron... more This paper considers a constrained version of the circle formation problem for a set of asynchronous, autonomous robots on the Euclidean plane. The circle formation problem asks a set of autonomous, mobile robots, initially having distinct locations, to place themselves, within finite time, at distinct locations on the circumference of a circle (not defined a priori), without colliding with each other. The constrained circle formation problem demands that in addition the maximum distance moved by any robot to solve the problem should be minimized. A basic objective of the optimization constrain is that it implies energy savings of the robots. This paper presents results in two parts. First, it is shown that the constrained circle formation problem is not solvable for oblivious asynchronous robots under ASYNC model even if the robots have rigid movements. Then the problem is studied for robots which have O(1) bits of persistent memory. The initial robot configurations, for which the ...

This paper addresses the constrained version of the mutual visibility problem for a set of asynch... more This paper addresses the constrained version of the mutual visibility problem for a set of asynchronous, opaque robots in the Euclidean plane. The mutual visibility problem asks the robots to form a configuration, within finite time and without collision, in which no three robots are collinear. The constrained mutual visibility problem in addition aims to minimize the maximum number of movements by a single robot. One of the implications of this constrained version of mutual visibility problem is that it also addresses issue of energy efficiency. The robots have a constant amount of persistent memory and they are equipped with externally visible lights which can assume a constant number of predefined colors. The colors represent different states of the robots and are used both for internal memory and communication. The colors of the lights do not change automatically. A distributed algorithm is proposed to solve the constrained mutual visibility problem for a set of asynchronous rob...