arXiv subjects

Rishi Ranjan Singh

Publications and source records attributed to Rishi Ranjan Singh.

7 recordsLinked to original sources

arXiv2026

Robust Treasure Hunt in Anonymous Graphs with Quantum Pebbles by Oblivious Agents

We study how to find a hidden treasure in anonymous graphs using an agent that has no persistent memory. The nodes are indistinguishable, and only edges have local port numbers. Classical pebbles placed by an oracle cannot guide an oblivious agent to the treasure. We introduce \emph{quantum pebbles}, which are sources that emit qubits in a fixed (unknown) state, encoding at every node the outgoing port on the shortest path to the treasure. By measuring in several non-orthogonal bases, an oblivious agent recovers the port and can reach the treasure in $D$ steps using $D$ quantum pebbles. This requires $O(Δ^{3}(\log D + \log Δ))$ measurements per node, where $Δ$ is the maximum degree. We further establish \emph{error robustness}, distinguishing two models of state preparation error. Under \emph{per-node persistent} error, where a device returns the same faulty encoding on every read, a single mislabelled coloured pebble can trap an oblivious agent in an infinite loop and every randomized strategy decays exponentially in $D$. Quantum pebbles inherit the same exponential decay. Under \emph{per-emission} error, the intended encoding is correct, but each emitted qubit independently changes state as $ρ= (1-e)\,\lvertψ\rangle\langleψ\rvert + e\,σ$ for an arbitrary noise matrix $σ$. Here the quantum protocol is provably robust. A threshold decoding rule with $O((\log D + \log Δ)/γ^{2})$ measurements per basis, where $γ= (1-e) - δ_e$ and $δ_e = (1-e)δ+ e$, has success probability close to $1$ as $D \to \infty$, provided $e < e^{*} = \sin^2(π/2Δ)/(1+\sin^2(π/2Δ))$. The separation that we establish is thus among quantum pebbles with per-emission error and a persistent marker.

quant-ph↗

arXiv2025

On the stress transit function

The stress interval $S(u,v)$ between $u,v\in V(G)$ is the set of all vertices in a graph $G$ that lie on every shortest $u,v$-path. A set $U \subseteq V(G)$ is stress convex if $S(u,v) \subseteq U$ for any $u,v\in U$. A vertex $v \in V(G)$ is s-extreme if $V(G)-v$ is a stress convex set in $G$. The stress number $sn(G)$ of $G$ is the minimum cardinality of a set $U$ where $\bigcup_{u,v \in U}S(u,v)=V(G)$. The stress hull number $sh(G)$ of $G$ is the minimum cardinality of a set whose stress convex hull is $V(G)$. In this paper, we present many basic properties of stress intervals. We characterize s-extreme vertices of a graph $G$ and construct graphs $G$ with arbitrarily large difference between the number of s-extreme vertices, $sh(G)$ and $sn(G)$. Then we study these three invariants for some special graph families, such as graph products, split graphs, and block graphs. We show that in any split graph $G$, $sh(G)=sn(G)=|Ext_s(G)|$, where $Ext_s(G)$ is the set of s-extreme vertices of $G$. Finally, we show that for $k \in \mathbb{N}$, deciding whether $sn(G) \leq k$ is NP-complete problem, even when restricted to bipartite graphs.

math.CO↗

arXiv2024

Forest Covers and Bounded Forest Covers

We study approximation algorithms for the forest cover and bounded forest cover problems. A probabilistic $2+ε$ approximation algorithm for the forest cover problem is given using the method of dual fitting. A deterministic algorithm with a 2-approximation ratio that rounds the optimal solution to a linear program is given next. The 2-approximation for the forest cover is then used to give a 6-approximation for the bounded forest cover problem. The use of the probabilistic method to develop the $2+ε$ approximation algorithm may be of independent interest.

cs.DS↗

arXiv2021

Temporal Analysis of Worldwide War

Analysis of wars and conflicts between regions has been an important topic of interest throughout the history of humankind. In the latter part of the 20th century, in the aftermath of two World Wars and the shadow of nuclear, biological, and chemical holocaust, more was written on the subject than ever before. Wars have a negative impact on a country's economy, social order, infrastructure, and public health. In this paper, we study the wars fought in history and draw conclusions from that. We explore the participation of countries in wars and the nature of relationships between various countries during different timelines. A big part of today's wars is fought against terrorism. Therefore, this study also attempts to shed light on different countries' exposure to terrorist encounters and analyses the impact of wars on a country's economy in terms of change in GDP.

econ.GN↗

arXiv2020

Centrality Measures: A Tool to Identify Key Actors in Social Networks

Experts from several disciplines have been widely using centrality measures for analyzing large as well as complex networks. These measures rank nodes/edges in networks by quantifying a notion of the importance of nodes/edges. Ranking aids in identifying important and crucial actors in networks. In this chapter, we summarize some of the centrality measures that are extensively applied for mining social network data. We also discuss various directions of research related to these measures.

cs.SI↗

arXiv2017

An Efficient Heuristic for Betweenness-Ordering

Centrality measures, erstwhile popular amongst the sociologists and psychologists, have seen broad and increasing applications across several disciplines of late. Amongst a plethora of application specific definitions available in the literature to rank the vertices, closeness centrality, betweenness centrality and eigenvector centrality (page-rank) have been the most important and widely applied ones. Networks where information, signal or commodities are flowing on the edges, surrounds us. Betweenness centrality comes as a handy tool to analyze such systems, but betweenness computation is a daunting task in large size networks. In this paper, we propose an efficient heuristic to determine the betweenness-ordering of $k$ vertices (where $k$ is very less than the total number of vertices) without computing their exact betweenness indices. The algorithm is based on a non-uniform node sampling model which is developed based on the analysis of Erdos-Renyi graphs. We apply our approach to find the betweenness-ordering of vertices in several synthetic and real-world graphs. The proposed heuristic results very efficient ordering even when runs for a linear time in the terms of the number of edges. We compare our method with the available techniques in the literature and show that our method produces more efficient ordering than the currently known methods.

cs.SI↗

arXiv2013

Navigability on Networks: A Graph Theoretic Perspective

Human navigation has been of interest to psychologists and cognitive scientists since the past few decades. It was in the recent past that a study of human navigational strategies was initiated with a network analytic approach, instigated mainly by Milgrams small world experiment. We brief the work in this direction and provide answers to the algorithmic questions raised by the previous study. It is noted that humans have a tendency to navigate using centers of the network - such paths are called the center-strategic-paths. We show that the problem of finding a center-strategic-path is an easy one. We provide a polynomial time algorithm to find a center-strategic-path between a given pair of nodes. We apply our finding in empirically checking the navigability on synthetic networks and analyze few special types of graphs.

cs.DS↗