arXiv subjects

Antika Sinha

Publications and source records attributed to Antika Sinha.

8 recordsLinked to original sources

arXiv2024

An Algorithm for the Decomposition of Complete Graph into Minimum Number of Edge-disjoint Trees

In this work, we study methodical decomposition of an undirected, unweighted complete graph ($K_n$ of order $n$, size $m$) into minimum number of edge-disjoint trees. We find that $x$, a positive integer, is minimum and $x=\lceil\frac{n}{2}\rceil$ as the edge set of $K_n$ is decomposed into edge-disjoint trees of size sequence $M = \{m_1,m_2,...,m_x\}$ where $m_i\le(n-1)$ and $Σ_{i=1}^{x} m_i$ = $\frac{n(n-1)}{2}$. For decomposing the edge set of $K_n$ into minimum number of edge-disjoint trees, our proposed algorithm takes total $O(m)$ time.

cs.DM↗

arXiv2024

Achieving Maximum Utilization in Optimal Time for Learning or Convergence in the Kolkata Paise Restaurant Problem

The objective of the KPR agents are to learn themselves in the minimum (learning) time to have maximum success or utilization probability ($f$). A dictator can easily solve the problem with $f = 1$ in no time, by asking every one to form a queue and go to the respective restaurant, resulting in no fluctuation and full utilization from the first day (convergence time $τ= 0$). It has already been shown that if each agent chooses randomly the restaurants, $f = 1 - e^{-1} \simeq 0.63$ (where $e \simeq 2.718$ denotes the Euler number) in zero time ($τ= 0$). With the only available information about yesterday's crowd size in the restaurant visited by the agent (as assumed for the rest of the strategies studied here), the crowd avoiding (CA) strategies can give higher values of $f$ but also of $τ$. Several numerical studies of modified learning strategies actually indicated increased value of $f = 1 - α$ for $α\to 0$, with $τ\sim 1/α$. We show here using Monte Carlo technique, a modified Greedy Crowd Avoiding (GCA) Strategy can assure full utilization ($f = 1$) in convergence time $τ\simeq eN$, with of course non-zero probability for an even larger convergence time. All these observations suggest that the strategies with single step memory of the individuals can never collectively achieve full utilization ($f = 1$) in finite convergence time and perhaps the maximum possible utilization that can be achieved is about eighty percent ($f \simeq 0.80$) in an optimal time $τ$ of order ten, even when $N$ the number of customers or of the restaurants goes to infinity.

cs.GT↗

arXiv2022

Development of research network on Quantum Annealing Computation and Information using Google Scholar data

We build and analyze the network of hundred top cited nodes (research papers and books from Google Scholar; strength or citation of the nodes range from about 44000 up to 100) starting early 1980 to till last year. These searched publications (papers, books) are based on Quantum Annealing Computation and Information categorized in four different sets: A) Quantum/Transverse Field Spin Glass Model, B) Quantum Annealing, C) Quantum Adiabatic Computation and D) Quantum Computation Information in the title or abstract of the searched publications. We fitted the growth in the annual number of publication ($n_p$) in each of these four categories A to D to the form $n_p \sim\exp{(t/τ)}$ where $t$ denotes the time in year. We found the scaling time $τ$ to be of order about 10 years for category A and C whereas $τ$ is order of about 5 years for category B and D.

physics.soc-ph↗

arXiv2022

Stochastic Learning in Kolkata Paise Restaurant Problem: Classical \& Quantum Strategies

We will review the results for stochastic learning strategies, both classical (one-shot and iterative) and quantum (one-shot only), for optimizing the available many-choice resources among a large number of competing agents, developed over the last decade in the context of the Kolkata Paise Restaurant Problem. Apart from a few rigorous and approximate analytical results, both for classical and quantum strategies, most of the interesting results on the phase transition behavior (obtained so far for the classical model) using classical Monte Carlo simulations. All these, including the applications to computer science (job or resource allotments in Internet-of-Things), transport engineering (on-line vehicle hire problems), operation research (optimizing efforts for delegated search problem, efficient solution of Travelling Salesman problem), etc will be discussed.

physics.soc-ph↗

arXiv2021

Development of Econophysics: A biased account and perspective from Kolkata

We present here a somewhat personalized account of the emergence of econophysics as an attractive research topic in physical as well as social sciences. After a rather detailed story telling about our endeavors from Kolkata, we give a brief description of the main research achievements in a simple and non-technical language. We also present briefly, in technical language, a piece of our recent research result. We conclude our paper with a brief perspective.

physics.soc-ph↗

arXiv2020

Phase transition in the Kolkata Paise Restaurant problem

A novel phase transition behaviour is observed in the Kolkata Paise Restaurant (KPR) problem where large number ($N$) of agents or customers collectively (and iteratively) learn to choose among the $N$ restaurants where she would expect to be alone that evening and would get the only dish available there (or may get randomly picked up if more than one agent arrive there that evening). The players are expected to evolve their strategy such that the publicly available information about past crowd in different restaurants can be utilized and each of them is able to make the best minority choice. For equally ranked restaurants we follow two crowd-avoiding strategies: Strategy I, where each of the $n_i(t)$ number of agents arriving at the $i$-th restaurant on the $t$-th evening goes back to the same restaurant on the next evening with probability $[n_i(t)]^{-α}$, while in Strategy II, with probability $p$, when $n_i(t) > 1$. We study the steady state ($t$-independent) utilization fraction $f:(1-f)$ giving the steady state (wastage) fraction of restaurants going without any customer in any particular evening. With both the strategies we find, near $α_c=0_+$ (in strategy I) or $p=1_-$ (in strategy II), the steady state wastage fraction $(1-f)\propto(α- α_c)^β$ or $(p_c - p)^β$ with $β\simeq 0.8, 0.87, 1.0$ and the convergence time $τ$ (for $f(t)$ becoming independent of $t$) varies as $τ\propto{(α-α_c)}^{-γ}$ or ${(p_c-p)}^{-γ}$, with $γ\simeq 1.18, 1.11, 1.05$ in infinite-dimension (rest of the $N-1$ neighboring restaurants), three-dimension ($6$ neighbors) and two-dimension ($4$ neighbors) respectively.

physics.soc-ph↗

arXiv2020

Econophysics Through Computation

We introduce here very briefly, through some selective choices of problems and through the sample computer simulation programs (following the request of the editor for this invited review in the Journal of Physics Through Computation), the newly developed field of econophysics. Though related attempts could be traced much earlier (see the Appendix), the formal researches in econophysics started in 1995. We hope, the readers (students \& researchers) can start themselves to enjoy the excitement, through the sample computer programs given, and eventually can undertake researches in the frontier problems, through the indicated survey literature provided.

physics.soc-ph↗

arXiv2019

Inequality in Death from Social Conflicts: A Gini & Kolkata indices-based Study

Human deaths caused by individual man-made conflicts (e.g., wars, armed-conflicts, terrorist-attacks etc.) occur unequally across the events (conflicts) and such inequality (in deaths) have been studied here using Lorenz curve and values of the inequality indices Gini ($g$) and Kolkata ($k$) have been estimated from it. The data are taken from various well-known databases maintained by some Universities and Peace Research Institutes. The inequality measures for man-made conflicts are found to have very high values ($g$ = $0.82 ~\pm~ $0.02, $k$ = $0.84~ \pm~ $0.02), which is rarely seen in economic (income or wealth) inequality measures across the world ($g \leq 0.4$, $k \leq 0.6$; presumably because of various welfare measures). We also investigated the inequalities in human deaths from natural disasters (like earthquakes, floods, etc.). Interestingly, we observe that the social inequality measures ($g$ and $k$ values) from man-made conflicts compare well with those of academic centers (inequality in citations; found in earlier studies) of different institutions of the world, while those for natural disasters can be even higher. We discuss about the `similarity classes' of social inequality (similar higher values of $g$ and $k$ indices) for man-made competitive societies like academic institutions and man-made social conflicts, and connect our observations with that of the growing recent trend of economic inequality across the world (with rapid disappearance of welfare strategies).

physics.soc-ph↗