arXiv subjects

Manoj Gupta

Publications and source records attributed to Manoj Gupta.

At least 19 recordsLinked to original sources

arXiv2026

$\tilde{O}$ptimal Algorithm for 2-Approximate All Pair Shortest Paths -- almost

Given an undirected, unweighted graph $G$, we aim to compute a 2-approximation of all-pairs shortest paths (APSP). This problem admits a natural lower bound of $\Omega(n^2)$ since the output size is $\Theta(n^2)$. A central goal in this area is to achieve a running time of $O(n^2)$. Dor, Halperin, and Zwick (FOCS 1996, SICOMP 2001) designed an algorithm with a running time of $\tilde{O}(n^2)$ that guarantees a 2-approximation only for pairs at a distance of at least $O(\log n)$. Recently, Gupta (FOCS 2025) improved this bound, handling all pairs at a distance of at least $O(\log \log n)$. We nearly resolve this problem. We design a randomized algorithm that runs in $\tilde{O}(n^2)$ time and, with high probability, guarantees a 2-approximation for all pairs at distance at least $c$, where $c \ge 0$ is a constant. Unlike the above two results, which were purely combinatorial, our algorithm combines combinatorial techniques with fast matrix multiplication (FMM).

cs.DS↗

arXiv2026

Approximate Single Source Dual Fault Tolerant Distance Oracle

We are given an undirected weighted graph $G$ with $n$ vertices and $m$ edges, edge weights in $[1, W]$, and a designated source vertex $s$. We design a single source dual fault tolerant distance oracle for $G$. Given a destination vertex $t$ and a set $F$ of at most two faulty edges, the oracle returns a $(1 + O(\epsilon))$-approximation of the weight of the shortest path from the source $s$ to $t$ avoiding $F$. Our oracle uses $\tilde{O}(n\sqrt{n})$ space and has $\tilde{O}(1)$ query time. Prior to our result, single source single fault tolerant oracles were known to return a $(1+\epsilon)$ approximation of the weight of the shortest path using $\tilde{O}(n)$ space and $O(1)$ query time. However, extending these approaches to multiple faults remained an open problem. Indeed, all $(1+\epsilon)$-approximate distance oracles that handle multiple faults require $\Omega(n^2)$ space. We break this bound by presenting the first dual fault tolerant distance oracle with $o(n^2)$ space.

cs.DS↗

arXiv2026

Two-orbital $e_g$ model with bond-dependent spin-orbit coupling: A playground for emergent band topology, Kitaev magnetism, and magnetoelectricity

Inspired by the electronic structure of compounds like nickel dihalides Ni$X_2$ ($X$=Cl, Br, I), we propose a low-energy two-orbital $e_g$ model featuring bond-dependent spin-orbit terms, driven by atomic spin-orbit coupling on the ligand $X$. We demonstrate that this model hosts a rich array of phenomena. In the non-interacting band limit, spin-orbit-derived spin-dependent and spin-flip hopping terms produce topological bands with spin-Chern numbers $C_s=\pm 2, \pm 4$, and higher order topological states with fractional corner charges, respectively. In the half-filled Mott insulator limit, we recover a spin-$1$ Hamiltonian with bond-dependent Kitaev exchange interactions. We explore the magnetoelectric effect in this two-orbital model using symmetry-based perspective and microscopic calculations, going beyond the generalized Katsura-Nagaosa-Balatsky theory for the single-orbital case. Our work may be relevant to study of doping, strain, or pressure on Ni$X_2$ and related materials.

cond-mat.str-el↗

arXiv2025

Multiple Dirac Spin-Orbital Liquids in SU(4) Heisenberg Antiferromagnets on the Honeycomb Lattice

We study the strong coupling model of $d^1$ transition metal tri-halides in the large spin-orbit coupled limit. By considering ab-initio-calculation-inspired hierarchy of hopping pathways of these compounds, SU(4) symmetry is found to emerge at multiple points in the parameter space of the hopping parameters. The resultant Dirac spin-orbital liquids, within the parton mean field description, are distinct. The calculated dynamical structure factor fingerprints this distinctive nature, giving rise to observable effects. This opens up a playground for SU(4) Dirac Spin-Orbital liquid in $d^1$ Honeycomb lattice systems.

cond-mat.str-el↗

arXiv2025

Improved 2-Approximate Shortest Paths for close vertex pairs

An influential result by Dor, Halperin, and Zwick (FOCS 1996, SICOMP 2000) implies an algorithm that can compute approximate shortest paths for all vertex pairs in $\tilde{O}(n^{2+O\left(\frac{1}{k}\right )})$ time, ensuring that the output distance is at most twice the actual shortest path, provided the pairs are at least $k$ apart, where $k \ge 2$. We present the first improvement on this result in over 25 years. Our algorithm achieves roughly same $\tilde{O}(n^{2+\frac{1}{k}})$ runtime but applies to vertex pairs merely $O(\log k)$ apart, where $\log k \ge 1$. When $k=\log n$, the running time of our algorithm is $\tilde{O}(n^2)$ and it works for all pairs at least $O(\log \log n)$ apart. Our algorithm is combinatorial, randomized, and returns correct results for all pairs with a high probability.

cs.DS↗

arXiv2025

Role of topotactic hydrogen in Superconductivity of Infinite-layer Nickelate NdNiO$_{2}$: A first-principles and variational Monte Carlo study

Employing combination of first-principles calculations, low-energy model construction, and variational Monte Carlo solution of the ab-initio derived Hubbard model, we study the effect of hydrogenation in the electronic structure and superconducting properties of infinite-layer nickelate, NdNiO$_2$. We find that the introduction of hydrogen at the apical oxygen vacancy position strongly influences the Wannier function corresponding to the effective interstitial orbital at the Ni site bound to the hydrogen. This results in the near disappearance of the electron pocket at the $k_z$ = $\pi$ Fermi surface, keeping that of $k_z$ = 0 unchanged, compared to the dehydrogenated case. The two-band model thus remains valid even in the presence of H. The calculated superconducting order parameters both in absence and presence of H, show a two-hump superconductivity arising the two overlapping domes, one arising from $d_{x^{2}-y^{2}}$ and another arising from interstitial orbital degree of freedom. Hydrogenation strengthens the latter, marginally affecting the former.

cond-mat.supr-con↗

arXiv2025

Electrically tunable Floquet Weyl photon emission from Dirac semimetal Cd3As2

The ability to optically engineer the Dirac band and electrically control the Fermi level in two-dimensional (2D) Dirac systems, such as graphene, has significantly advanced quantum technologies. However, similar tunability has remained elusive in three-dimensional Dirac systems. In this work, we demonstrate both optical and electrical tunability of the band structure in the 3D Dirac semimetal Cd3As2. Photoexcitation with circularly polarized light breaks time-reversal symmetry, lifting the degeneracy at Dirac points to transform the material into a Floquet Weyl semimetal with chiral Weyl nodes. This transition induces nonzero Berry curvature, giving rise to helicity-dependent transverse anomalous photocurrents, detectable through terahertz emission at normal incidence. Furthermore, applying an external electric field displaces the Fermi level away from the Dirac point, enlarging the Dirac cone projection leading to a reduced density of states of Fermi arcs. As a result, we achieve precise electrical control over Floquet band engineering, resulting in a large modulation of THz emission. Moreover, at oblique incidence, the circular photon-drag effect induces helicity-dependent longitudinal photocurrents. Simultaneous generation and manipulation of both longitudinal and transverse photocurrents enable precise control of the helicity of emitted THz pulses. These results pave the way for electric field-controlled Floquet Weyl THz sources, offering significant potential for applications in quantum computing and low-power electronics.

cond-mat.mtrl-sci↗

arXiv2024

Near Optimal Dual Fault Tolerant Distance Oracle

We present a dual fault-tolerant distance oracle for undirected and unweighted graphs. Given a set $F$ of two edges, as well as a source node $s$ and a destination node $t$, our oracle returns the length of the shortest path from $s$ to $t$ that avoids $F$ in $O(1)$ time with a high probability. The space complexity of our oracle is $\Tilde{O}(n^2)$ \footnote{$\Tilde{O}$ hides poly$\log n$ factor }, making it nearly optimal in terms of both space and query time. Prior to our work, Pettie and Duan [SODA 2009] designed a dual fault-tolerant distance oracle that required $\Tilde{O}(n^2)$ space and $O(\log n)$ query time. In addition to improving the query time, our oracle is much simpler than the previous approach.

cs.DS↗

arXiv2024

Inter-chain Interactions, Multi-magnon condensation and Strain effect in chain compound NaVOPO$_4$

Employing first-principles modelling and many-body methods, the magnetic properties of spin-1/2 chain compound NaVOPO$_4$ are explored. The extensive first-principles calculations establish an intricate three-dimensionally coupled model that consists of weakly alternating $J$-$J^{\prime}$ antiferromagnetic chains running along cris-cross directions between two consecutive $ab$ planes, connected via two subleading couplings, a ferromagnetic exchange along the $c$ direction ($J_c$) and a weaker antiferromagnetic exchange ($J_a$) along the body diagonal direction. The exact diagonalization and density matrix renormalized group study has been carried out on a two-dimensional spin model with $J$-$J^{\prime}$-$J_c$ and effective $J_d$ couplings, constructed based on the full model, for numerical ease. The $J_c$-$J_d$ phase diagram is found to host a {\it disorder} phase with a finite spin gap for comparable values of $J_c$ and $J_d$, arising out of the competing nature of these two interactions, other than two ordered phases. The calculated thermodynamic properties of this model provide a fair description of experimentally measured data. The predominant manifestation of $J_c$ and $J_d$ in the disorder phase happens in the stabilisation of a multi-magnon condensed phase, upon gap closing by application of an external magnetic field. We further explore the effect of tensile uniaxial strain, which is found to drive the system from gapful to gapless ground state.

cond-mat.str-el↗

arXiv2024

Nearly Optimal Fault Tolerant Distance Oracle

We present an $f$-fault tolerant distance oracle for an undirected weighted graph where each edge has an integral weight from $[1 \dots W]$. Given a set $F$ of $f$ edges, as well as a source node $s$ and a destination node $t$, our oracle returns the \emph{shortest path} from $s$ to $t$ avoiding $F$ in $O((cf \log (nW))^{O(f^2)})$ time, where $c > 1$ is a constant. The space complexity of our oracle is $O(f^4n^2\log^2 (nW))$. For a constant $f$, our oracle is nearly optimal both in terms of space and time (barring some logarithmic factor).

cs.DS↗

arXiv2023

The Group Access Bounds for Binary Search Trees

The access lemma (Sleator and Tarjan, JACM 1985) is a property of binary search trees that implies interesting consequences such as static optimality, static finger, and working set property. However, there are known corollaries of the dynamic optimality that cannot be derived via the access lemma, such as the dynamic finger, and any $o(\log n)$-competitive ratio to the optimal BST where $n$ is the number of keys. In this paper, we introduce the group access bound that can be defined with respect to a reference group access tree. Group access bounds generalize the access lemma and imply properties that are far stronger than those implied by the access lemma. For each of the following results, there is a group access tree whose group access bound Is $O(\sqrt{\log n})$-competitive to the optimal BST. Achieves the $k$-finger bound with an additive term of $O(m \log k \log \log n)$ (randomized) when the reference tree is an almost complete binary tree. Satisfies the unified bound with an additive term of $O(m \log \log n)$. Matches the unified bound with a time window $k$ with an additive term of $O(m \log k \log \log n)$ (randomized). Furthermore, we prove simulation theorem: For every group access tree, there is an online BST algorithm that is $O(1)$-competitive with its group access bound. In particular, any new group access bound will automatically imply a new BST algorithm achieving the same bound. Thereby, we obtain an improved $k$-finger bound (reference tree is an almost complete binary tree), an improved unified bound with a time window $k$, and matching the best-known bound for Unified bound in the BST model. Since any dynamically optimal BST must achieve the group access bounds, we believe our results provide a new direction towards proving $o(\log n)$-competitiveness of Splay tree and Greedy.

cs.DS↗

arXiv2023

On-chip Amorphous THz Topological Photonic Interconnects

Valley Hall photonic crystals (VPCs) offer the potential to create topological waveguides capable of guiding light through sharp bends on a chip. They can seamlessly integrate with functional components while occupying minimal space, making them a promising technology for terahertz (THz) topological photonic integrated circuits. However, a significant limitation for THz-scale integrated VPC-based devices has been the absence of arbitrary bend interconnects. Due to the crystalline symmetry, the traditional VPC designs restrict waveguides to the principal lattice axes (i.e., only 0-, 60- or 120- degree orientations). Here, we present an on-chip, all silicon implementation of deformed VPCs enabling topological waveguides with a variety of shapes and bends. Although the lattice is amorphous and lacks long-range periodicity, the topological protection of the waveguides is sustained by short-range order. We experimentally demonstrate the robust on-chip transmission of THz waves through waveguides of complicated shapes and arbitrary bends. We implement an amorphous lattice that serves as a frequency-dependent router capable of splitting the input signal into two perpendicular output ports, which cannot be achieved with an undeformed VPC. In addition, we showcase on-chip THz communication through 90 degree and P-shaped VPC waveguides, achieving data rates of 72 Gbit/s and 32 Gbit/s, respectively. Our findings demonstrate that the amorphous topological photonic crystals significantly enhance the adaptability of on-chip interconnections while preserving the performance of the topological waveguides.

physics.optics↗

arXiv2023

Ab-initio Insights on the Fermiology of $d^1$ Transition metals in Honeycomb lattice : Hierarchy of hopping pathways and spin-orbit coupling

Motivated by the intriguing suggestion of realizing SU(8) Dirac semi-metal with $J=3/2$ electrons on a honeycomb lattice, we provide a systematic study of the interplay of various hopping pathways and atomic spin-orbit coupling for the low energy electrons in candidate d$^1$ transition metal halides MX$_3$ (M=Ti, Zr, Hf; X=F, Cl, Br). By combining first principle calculations and minimal hopping Hamiltonian, we uncover the role of dominant direct metal-metal hopping on top of indirect metal-halide-metal hopping. This sets up a hierarchy of hopping pathways that centrally modify the SU(8) picture for the above materials. These hopping interactions, along with the spin-orbit coupling, lead to a plethora of exactly compensated metals instead of the SU(8) Dirac semi-metal. Remarkably the same can be understood as descendants of a topological insulator obtained by gapping out the SU(8) Dirac semi-metallic phase. The resultant compensated metals have varied Fermi surface topology and are separated by Lifshitz phase transitions. We discuss the implications of the proximate Lifshitz transition, which may be accessed via strain, in the context of the relevant materials.

cond-mat.str-el↗

arXiv2022

Improved Pattern-Avoidance Bounds for Greedy BSTs via Matrix Decomposition

Greedy BST (or simply Greedy) is an online self-adjusting binary search tree defined in the geometric view ([Lucas, 1988; Munro, 2000; Demaine, Harmon, Iacono, Kane, Patrascu, SODA 2009). Along with Splay trees (Sleator, Tarjan 1985), Greedy is considered the most promising candidate for being dynamically optimal, i.e., starting with any initial tree, their access costs on any sequence is conjectured to be within $O(1)$ factor of the offline optimal. However, in the past four decades, the question has remained elusive even for highly restricted input. In this paper, we prove new bounds on the cost of Greedy in the ''pattern avoidance'' regime. Our new results include: The (preorder) traversal conjecture for Greedy holds up to a factor of $O(2^{\alpha(n)})$, improving upon the bound of $2^{\alpha(n)^{O(1)}}$ in (Chalermsook et al., FOCS 2015). This is the best known bound obtained by any online BSTs. We settle the postorder traversal conjecture for Greedy. The deque conjecture for Greedy holds up to a factor of $O(\alpha(n))$, improving upon the bound $2^{O(\alpha(n))}$ in (Chalermsook, et al., WADS 2015). The split conjecture holds for Greedy up to a factor of $O(2^{\alpha(n)})$. Key to all these results is to partition (based on the input structures) the execution log of Greedy into several simpler-to-analyze subsets for which classical forbidden submatrix bounds can be leveraged. Finally, we show the applicability of this technique to handle a class of increasingly complex pattern-avoiding input sequences, called $k$-increasing sequences. As a bonus, we discover a new class of permutation matrices whose extremal bounds are polynomially bounded. This gives a partial progress on an open question by Jacob Fox (2013).

cs.DS↗

arXiv2022

The Elusive High-Tc Superinductor

Ginzburg-Landau (GL) parameters formed the basis for Abrikosov discovery of the quantum vortex of a supercurrent in type-II superconductor with a normal core of size $\xi$, the superconductor coherence length and circulating supercurrent induced magnetic field diverging as $log(1/r)$ from the core with a decay length of the London penetration depth, $\lambda_L.$ In 1964, J. Pearl predicted the slowly decaying $(1/r^2)$ field around a vortex spreading out to Pearl length, $P_L=2\lambda_L^2/t$, in a superconductor film of thickness $t < \lambda_L$. However, his quintessential theory failed to predict the existence of giant kinetic inductance (GKI) that arises from the enlarged screening currents of the vortex. Here, we discover giant kinetic inductance in a $high-T_c$ metasurface due to the 1400% expansion of the vortex screening supercurrent from $\lambda_L$ to 14$\lambda_L$ in ultrathin film meta-atom of $\lambda_L/7$ thickness, which leads to the emergence of terahertz superinductance possessing quantum impedance exceeding the resistance quantum limit of $R_Q=h/(2e)^2 =6.47 k\Omega$ by 33%. Our discovery presents a new class of $high-T_c$ superconductor electronic, photonic, and quantum devices enabled through metasurface designed at the Pearl length scales, providing novel applications in quantum circuitry, metrology, and single photon kinetic inductance detectors.

cond-mat.supr-con↗

arXiv2022

Near Optimal Algorithm for Fault Tolerant Distance Oracle and Single Source Replacement Path problem

In a graph $G$ with a source $s$, we design a distance oracle that can answer the following query: Query$(s,t,e)$ -- find the length of shortest path from a fixed source $s$ to any destination vertex $t$ while avoiding any edge $e$. We design a deterministic algorithm that builds such an oracle in $\tilde{O}(m\sqrt n)$ time. Our oracle uses $\tilde{O}(n\sqrt n)$ space and can answer queries in $\tilde{O}(1)$ time. Our oracle is an improvement of the work of Bil\`{o} et al. (ESA 2021) in the preprocessing time, which constructs the first deterministic oracle for this problem in $\tilde{O}(m\sqrt n+n^2)$ time. Using our distance oracle, we also solve the {\em single source replacement path problem} (SSR problem). Chechik and Cohen (SODA 2019) designed a randomized combinatorial algorithm to solve the SSR problem. The running time of their algorithm is $\tilde{O}(m\sqrt n + n^2)$. In this paper, we show that the SSR problem can be solved in $\tilde{O}(m\sqrt n + |\mathcal{R}|)$ time, where $\mathcal{R}$ is the output set of the SSR problem in $G$. Our SSR algorithm is optimal (upto polylogarithmic factor) as there is a conditional lower bound of $\Omega(m\sqrt n)$ for any combinatorial algorithm that solves this problem.

cs.DS↗

arXiv2020

Multiple Source Replacement Path Problem

One of the classical line of work in graph algorithms has been the Replacement Path Problem: given a graph $G$, $s$ and $t$, find shortest paths from $s$ to $t$ avoiding each edge $e$ on the shortest path from $s$ to $t$. These paths are called replacement paths in literature. For an undirected and unweighted graph, (Malik, Mittal, and Gupta, Operation Research Letters, 1989) and (Hershberger and Suri, FOCS 2001) designed an algorithm that solves the replacement path problem in $\tilde O(m+n)$ time. It is natural to ask whether we can generalize the replacement path problem: {\em can we find all replacement paths from a source $s$ to all vertices in $G$?} This problem is called the Single Source Replacement Path Problem. Recently (Chechik and Cohen, SODA 2019) designed a randomized combinatorial algorithm that solves the Single Source Replacement Path Problem in $\tilde O(m\sqrt n\ + n^2)$ time. One of the questions left unanswered by their work is the case when there are many sources, not one. When there are $n$ sources, the combinatorial algorithm of (Bernstein and Karger, STOC 2009) can be used to find all pair replacement path in $\tilde O(mn + n^3)$ time. However, there is no result known for any general $\sigma$. Thus, the problem we study is defined as follows: given a set of $\sigma$ sources, we want to find the replacement path from these sources to all vertices in $G$. We give a randomized combinatorial algorithm for this problem that takes $\tilde O(m\sqrt{n \sigma} +\ \sigma n^2)$ time. This result generalizes both results known for this problem. Our algorithm is much different and arguably simpler than (Chechik and Cohen, SODA 2019). Like them, we show a matching conditional lower bound using the Boolean Matrix Multiplication conjecture.

cs.DS↗

arXiv2019

Terahertz sensing of 7nm dielectric film with bound states in the continuum metasurfaces

Fingerprint spectral response of several materials with terahertz electromagnetic radiation indicates that terahertz technology is an effective tool for sensing applications. However, sensing few nanometer thin-film of dielectrics with much longer terahertz waves (1 THz = 0.3 mm) is challenging. Here, we demonstrate a quasi-bound state in the continuum (BIC) resonance for sensing of nanometer scale thin analyte deposited on a flexible metasurface. The large sensitivity originates from strong local field confinement of the quasi-BIC Fano resonance state and extremely low absorption loss of a low-index cyclic olefin copolymer substrate. A minimum thickness of 7 nm thin-film of germanium is sensed on the metasurface, which corresponds to a deep subwavelength length scale of {\lambda}/43000, where {\lambda} is the resonance wavelength. The low-loss, flexible and large mechanical strength of the quasi-BIC micro structured metamaterial sensor could be an ideal platform for developing ultrasensitive wearable terahertz sensors.

physics.optics↗