arXiv subjects

Subhajit Pramanick

Publications and source records attributed to Subhajit Pramanick.

8 recordsLinked to original sources

arXiv2026

Short Graph Sketches Suffice for Error-resilient Leader Verification in CONGEST

Locally Checkable Proofs (LCPs) enable the verification of global graph properties using locally checkable certificates assigned by a prover. Recently, this framework was extended to Locally Checkable Proofs-with-Errors (LCPE), where an adversary may corrupt some certificates. Existing LCPE algorithms, however, are designed for the LOCAL model, whose unbounded communication makes them unsuitable for direct implementation in the bandwidth-restricted CONGEST model. We initiate the study of efficient CONGEST implementations of LCPE through the \textsc{unique-leader} verification problem on trees. The main challenge is that tolerating $\varepsilon$ certificate errors requires each node to reason about its $(2\varepsilon+1)$-hop neighborhood, whose exact topology may require up to $O(\Delta^{2\varepsilon+1}\log n)$ bits to communicate. To overcome this bottleneck, we introduce \emph{local graph sketches}, together with the notions of \emph{imagined trees} and \emph{imagined certifications}, which encode precisely the information needed for verification using only $O(\varepsilon^2\log n)$ bits per node. Based on these sketches, we design an LCPE algorithm that tolerates up to $\varepsilon$ adversarial certificate errors and constructs the required sketches in $O(\varepsilon^2)$ communication rounds in the CONGEST model. We complement our algorithm with a matching impossibility result: even in the strictly more powerful LOCAL model, and even with unbounded certificate size, no verification scheme with view distance at most $\varepsilon$ can tolerate $\varepsilon$ adversarial certificate errors. Since every CONGEST algorithm can be simulated in LOCAL, this lower bound immediately applies to CONGEST, showing that a view distance exceeding $\varepsilon$ is unavoidable.

cs.DC↗

arXiv2026

Observation of intertwined charge density wave order and superconductivity in Janus monolayer

Low-dimensional transition-metal dichalcogenides (TMDCs) provide an ideal platform for studying the emergence of charge density wave (CDW) and superconductivity. The discovery of emergent CDW order in 1T $\mathrm{ZrTe_2}$ monolayer raises an important question: does this instability persist when one $\mathrm{Te}$ chalcogen layer is substituted by $\mathrm{Se}$? In the present work, we investigate the CDW (2$\times$2$\times$1) and superconducting instability in 1T $\mathrm{ZrSeTe}$ Janus monolayer using first-principles calculations. The phonon spectrum exhibits a pronounced anomaly at the $\mathrm{M}$ point of the irreducible Brillouin zone, arising from enhanced electron-phonon interaction together with electronic instabilities originating from both interband and intraband scattering. The resulting lattice distortion reconstructs the electronic structure, opening a small indirect band gap, driving the system from a semi-metallic to a semiconducting state. The energy gain associated with the distortion is significantly smaller than that of $\mathrm{ZrTe_2}$ monolayer, indicating that the replacement of one $\mathrm{Te}$ chalcogen layer with $\mathrm{Se}$ weakens the CDW instability. We have further investigated the effects of electronic correlation and biaxial strain, both acts as effective tuning parameters for the instabilities concerened. In the high temperature undistorted phase, $\mathrm{ZrSeTe}$ exhibits phonon mediated two-gap superconductivity. It originates primarily from the robust coupling between the soft phonon mode at $\mathrm{M}$ point and the electronic bands predominantly derived from $\mathrm{Zr}$ $\mathit{d}$ and $\mathrm{Te}$ $\mathit{p}$ orbitals crossing the Fermi level. Spin-orbit coupling (SOC) further modifies the electronic states and reduces the superconducting transition temperature.

cond-mat.supr-con↗

arXiv2026

Distributed Local Verification using Proofs with(out) Errors

We study local verification of graph properties in distributed networks under the framework of \emph{locally checkable proofs} (LCPs). In an LCP, a prover assigns proof labels to nodes, and a distributed verifier must make all nodes accept if the graph satisfies the property, while at least one node rejects otherwise. Each node bases its decision on a local neighborhood, called its \emph{view distance}. Our focus is twofold. First, we study cycle existence, i.e., whether a graph contains a cycle (as opposed to cycle-freeness). We show that cycle existence admits verification with only $3$ proof labels and view distance $1$, and establish a matching lower bound. More importantly, inspired by direction-encoding techniques based on BFS distances, we introduce a novel gadget that encodes direction using only $2$ labels and view distance $3$ through repeated occurrences of the string $001101$. Although developed for cycle existence, this gadget may be useful for other verification tasks. Second, we introduce an \emph{erroneous proof} model in which an adversary may corrupt proof labels of at most $i$ nodes within the $(2i+1)$-hop neighborhood of each node. We present an algorithmic framework, called \textbf{\texttt{refix}}, that transforms an error-free verifier into one that tolerates such errors at the cost of a view distance of $2i+1$. We demonstrate the framework on cycle existence, cycle-freeness, and bipartiteness, and establish lower bounds relating the number of errors to the required view distance. Finally, we show that our $2$-label, view-distance-$3$ verifier for cycle existence admits a $3$-round implementation in the \textsc{CONGEST} model, providing a first step toward implementing LCPs under communication constraints.

cs.DC↗

arXiv2025

Asynchronous Gathering of Opaque Robots with Mobility Faults

We consider the fundamental benchmarking problem of gathering in an $(N,f)$-fault system consisting of $N$ robots, of which at most $f$ might fail at any execution, under asynchrony. Two seminal results established impossibility of a solution in the oblivious robot (OBLOT) model in a $(2,0)$-fault system under semi-synchrony and in a $(3,1)$-Byzantine fault system under asynchrony. Recently, a breakthrough result circumvented the first impossibility result by giving a deterministic algorithm in a $(2,0)$-fault system under asynchrony in the luminous robot (LUMI) model using 2-colored lights. However, a breakthrough result established impossibility of gathering in a $(2,1)$-crash system in the LUMI model under semi-synchrony. In this paper, we consider a {\em mobility fault} model in which a robot crash only impacts it mobility but not the operation of the light. We establish four results under asynchrony in LUMI with the mobility fault model. We show that it is impossible to solve gathering in a $(2,1)$-mobility fault system using 2-colored lights, and then give a solution using 3-colored lights, which is optimal w.r.t. the number of colors. We then consider an $(N,f)$-mobility fault system, $f<N$, both $N,f$ not known, and give two deterministic algorithms that exhibit a nice time-color trade-off: The first with time $O(N)$ using 7-colored lights and the second with time $O(\max\{\ell,f\})$ using 26-colored lights, where $\ell< N$ is the number of distinct convex layers of robot positions in the initial configuration. Interestingly, for $l, f = O(1)$, our result is optimal. Our algorithms for an $(N,f)$-mobility fault system are the first to be analysed time complexity, can withstand obstructed visibility (opaque robot model) and asynchronous scheduling.

cs.DC↗

arXiv2025

Time-optimal Asynchronous Minimal Vertex Covering by Myopic Robots

In a connected graph with an autonomous robot swarm with limited visibility, it is natural to ask whether the robots can be deployed to certain vertices satisfying a given property using only local knowledge. This paper affirmatively answers the question with a set of \emph{myopic} (finite visibility range) luminous robots with the aim of \emph{filling a minimal vertex cover} (MVC) of a given graph $G = (V, E)$. The graph has special vertices, called \emph{doors}, through which robots enter sequentially. Starting from the doors, the goal of the robots is to settle on a set of vertices that forms a minimal vertex cover of $G$ under the asynchronous ($\mathcal{ASYNC}$) scheduler. We are also interested in achieving the \emph{minimum vertex cover} (MinVC, which is NP-hard \cite{Karp1972} for general graphs) for a specific graph class using the myopic robots. We establish lower bounds on the visibility range for the robots and on the time complexity (which is $\Omega(|E|)$). We present two algorithms for trees: one for single door, which is both time and memory-optimal, and the other for multiple doors, which is memory-optimal and achieves time-optimality when the number of doors is a constant. Interestingly, our technique achieves MinVC on trees with a single door. We then move to the general graph, where we present two algorithms, one for the single door and the other for the multiple doors with an extra memory of $O(\log \Delta)$ for the robots, where $\Delta$ is the maximum degree of $G$. All our algorithms run in $O(|E|)$ epochs.

cs.DC↗

arXiv2025

Pressure induced evolution of anisotropic superconductivity and Fermi surface nesting in a ternary boride

Using Migdal-Eliashberg theory implemented in Electron Phonon Wannier (EPW) code, we have investigated anisotropic superconductivity in a ternary boride $\mathrm{Ta(MoB)_2}$. It is a single-gap, anisotropic, phonon-mediated superconductor having a critical temperature $\mathrm{T_c}\sim \, 19.3$ K. A dominant contribution to superconductivity arises from the robust coupling between electronic states, primarily created by the $\mathrm{d_{xy}}$,$\mathrm{d_{x^2 - y^2}}$ orbitals of Mo atoms and the in-plane vibrations of Mo atoms. A weak Fermi surface nesting and a small electron-phonon coupling cannot induce charge density wave-like instabilities, as evidenced by the lack of a significant peak in the real part of the total Lindhard susceptibility and the absence of phonon softening. Furthermore, we have studied its electronic and superconducting properties under hydrostatic pressure up to 76.69 GPa, owing to its low bulk modulus and metastability. The persistent reduction in the density of states at the Fermi level, Fermi surface nesting and the stiffening of phonon modes lead to a diminution of superconductivity under pressure up to 59.71 GPa. At 76.69 GPa, a modification in the topology of the Fermi surface, namely a Lifshitz transition, occurs resulting in a sudden enhancement of nesting. This enhanced nesting, in turn, induces an abrupt stabilisation of superconductivity at 76.69 GPa, resulting in a V-shaped response to pressure.

cond-mat.supr-con↗

arXiv2024

Uniform Partitioning of a Bounded Region using Opaque ASYNC Luminous Mobile Robots

We are given $N$ autonomous mobile robots inside a bounded region. The robots are opaque which means that three collinear robots are unable to see each other as one of the robots acts as an obstruction for the other two. They operate in classical \emph{Look-Compute-Move} (LCM) activation cycles. Moreover, the robots are oblivious except for a persistent light (which is why they are called \emph{Luminous robots}) that can determine a color from a fixed color set. Obliviousness does not allow the robots to remember any information from past activation cycles. The Uniform Partitioning problem requires the robots to partition the whole region into sub-regions of equal area, each of which contains exactly one robot. Due to application-oriented motivation, we, in this paper consider the region to be well-known geometric shapes such as rectangle, square and circle. We investigate the problem in \emph{asynchronous} setting where there is no notion of common time and any robot gets activated at any time with a fair assumption that every robot needs to get activated infinitely often. To the best of our knowledge, this is the first attempt to study the Uniform Partitioning problem using oblivious opaque robots working under asynchronous settings. We propose three algorithms considering three different regions: rectangle, square and circle. The algorithms proposed for rectangular and square regions run in $O(N)$ epochs whereas the algorithm for circular regions runs in $O(N^2)$ epochs, where an epoch is the smallest unit of time in which all robots are activated at least once and execute their LCM cycles. The algorithms for the rectangular, square and circular regions require $2$ (which is optimal), $5$ and $8$ colors, respectively.

cs.DC↗

arXiv2022

Filling MIS Vertices by Myopic Luminous Robots

We present the problem of finding a maximal independent set (MIS) (named as \emph{MIS Filling problem}) of an arbitrary connected graph having $n$ vertices with luminous myopic mobile robots. The robots enter the graph one after another from a particular vertex called the \emph{Door} and disperse along the edges of the graph without collision to occupy vertices such that the set of vertices occupied by the robots is a maximal independent set. We assume the robots have knowledge only about the maximum degree of the graph, denoted by $Δ$. In this paper, we explore two versions of the problem: the solution to the first version, named as \emph{MIS Filling with Single Door}, works under an asynchronous scheduler using robots with 3 hops of visibility range, $Δ+ 6$ number of colors and $O(\log Δ)$ bits of persistent storage. The time complexity is measured in terms of epochs and it can be solved in $O(n^2)$ epochs. An epoch is the smallest time interval in which each participating robot gets activated and executes the algorithm at least once. For the second version with $k~ ( > 1)$ \textit{Doors}, named as \emph{MIS Filling with Multiple Doors}, the solution works under a semi-synchronous scheduler using robots with 5 hops of visibility range, $Δ+ k + 6$ number of colors and $O(\log (Δ+ k))$ bits of persistent storage. The problem with multiple Doors can be solved in $O(n^2)$ epochs.

cs.DC↗