arXiv subjects

Mihir Hasabnis

Publications and source records attributed to Mihir Hasabnis.

6 recordsLinked to original sources

arXiv2026

Impact of Iterative Fine-Tuning on Transcription Accuracy in Complex Historical Sanskrit Manuscripts

Digitizing the text from handwritten historical manuscripts is required to make them easily accessible, preservable, and to enable historical scholars to study them in new ways. Historical manuscripts, however, often exhibit complex heterogeneous layouts and non-standard appearance due to period-specific writing styles, page textures, camera noise, and other nuisance factors, making them difficult to perform OCR on. To tackle this challenge, we introduce a local traditional OCR pipeline, which can be iteratively fine-tuned on the target manuscript at the layout-level and the appearance-level. By adapting to the target manuscript distribution, the proposed Traditional OCR pipeline makes better predictions on subsequent pages, causing iterative reduction in human annotation effort, which is expensive and time-consuming as it requires historical domain expertise. Using this pipeline, we digitize text from three complex historical Sanskrit manuscripts and introduce a dataset with granular layout-level annotations, along with Unicode annotations in the standard PAGE-XML format. We demonstrate quantitative gains due to iterative fine-tuning of the proposed traditional OCR pipeline, and also benchmark the performance of leading Multi-Modal Large Language Models on the introduced Dataset. Code and dataset are available at: https://github.com/flame-cai/gnn-synthetic-layout-historical/.

cs.CV↗

arXiv2022

Colorful Hamilton cycles in random graphs

Given an $n$ vertex graph whose edges have colored from one of $r$ colors $C=\{c_1,c_2,\ldots,c_r\}$, we define the Hamilton cycle color profile $hcp(G)$ to be the set of vectors $(m_1,m_2,\ldots,m_r)\in [0,n]^r$ such that there exists a Hamilton cycle that is the concatenation of $r$ paths $P_1,P_2,\ldots,P_r$, where $P_i$ contains $m_i$ edges of color $c_i$. We study $hcp(G_{n,p})$ when the edges are randomly colored. We discuss the profile close to the threshold for the existence of a Hamilton cycle and the threshold for when $hcp(G_{n,p})=\{(m_1,m_2,\ldots,m_r)\in [0,n]^r: m_1+m_2+\cdots+m_r=n\}$.

math.CO↗

arXiv2021

Minimizing the number of edges in $K_{s,t}$-saturated bipartite graphs

This paper considers an edge minimization problem in saturated bipartite graphs. An $n$ by $n$ bipartite graph $G$ is $H$-saturated if $G$ does not contain a subgraph isomorphic to $H$ but adding any missing edge to $G$ creates a copy of $H$. More than half a century ago, Wessel and Bollobás independently solved the problem of minimizing the number of edges in $K_{(s,t)}$-saturated graphs, where $K_{(s,t)}$ is the `ordered' complete bipartite graph with $s$ vertices from the first color class and $t$ from the second. However, the very natural `unordered' analogue of this problem was considered only half a decade ago by Moshkovitz and Shapira. When $s=t$, it can be easily checked that the unordered variant is exactly the same as the ordered case. Later, Gan, Korándi, and Sudakov gave an asymptotically tight bound on the minimum number of edges in $K_{s,t}$-saturated $n$ by $n$ bipartite graphs, which is only smaller than the conjecture of Moshkovitz and Shapira by an additive constant. In this paper, we confirm their conjecture for $s=t-1$ with the classification of the extremal graphs. We also improve the estimates of Gan, Korándi, and Sudakov for general $s$ and $t$, and for all sufficiently large $n$.

math.CO↗

arXiv2021

Isomorphism for Random $k$-Uniform Hypergraphs

We study the isomorphism problem for random hypergraphs. We show that it is solvable in polynomial time for the binomial random $k$-uniform hypergraph $H_{n,p;k}$, for a wide range of $p$. We also show that it is solvable w.h.p. for random $r$-regular, $k$-uniform hypergraphs $H_{n,r;k},r=O(1)$.

math.CO↗

arXiv2020

The threshold for the full perfect matching color profile in a random coloring of random graphs

Consider a graph $G$ with a coloring of its edge set $E(G)$ from a set $Q = \set{c_1,c_2, \ldots, c_q}$. Let $Q_i$ be the set of all edges colored with $c_i$. Recently, Frieze defined a notion of the perfect matching color profile denoted by $\mcp(G)$, which is the set of vectors $(m_1, m_2, \ldots, m_q) \in [n]^q$ such that there exists a perfect matching $M$ in $G$ with $|Q_i \cap M| = m_i$ for all $i$. Let $\a_1, \a_2, \ldots, \a_q$ be positive constants such that $\sum_{i=1}^q \a_i = 1$. Let $G$ be the random bipartite graph $G_{n,n,p}$. Suppose the edges of $G$ are independently colored with color $c_i$ with probability $α_i$. We determine the threshold for the event $\mcp(G) = \set{(m_1, \ldots, m_q) \in [0,n]^q : m_1 + \cdots + m_q = n}$, answering a question posed by Frieze. We further extend our methods to find the threshold for the same event in a randomly colored random graph $G_{n,p}$.

math.CO↗

arXiv2019

The game chromatic number of a random hypergraph

We consider the following game, played on a $k$-uniform hypergraph $H$. There are $q$ colors available and two players take it in turns to color vertices. A partial coloring is proper if no edge is mono-chromatic. One player, A, wishes to color all the vertices and the other player, B, wishes to prevent this. The {\em game chromatic number} $χ_g(H)$ is the minimum number of colors for which A has a winning strategy. We consider this in the context of a random $k$-uniform hypergraph and prove upper and lower bounds that hold w.h.p.

math.CO↗