arXiv subjects

Ritam Manna Mitra

Publications and source records attributed to Ritam Manna Mitra.

2 recordsLinked to original sources

arXiv2026

Solving Vertex Integrity Faster than $2^n$

Vertex Integrity is a classical graph parameter measuring the vulnerability of a network to vertex failures. We settle two fundamental questions concerning its exact exponential complexity. First, we prove that, unless the Exponential Time Hypothesis fails, Vertex Integrity has no $2^{o(n)}n^{O(1)}$-time algorithm. Secondly, we give a deterministic exact algorithm running in $O(1.9602^n)$ time and space, improving the straightforward $O(2^n)$ bound.

cs.DS↗

arXiv2026

Minimum eccentricity shortest paths of $K_{2,3}$-minor-free graphs

Given a simple, undirected, and unweighted graph $G$, and an integer $R$, the objective of the \textsc{Minimum Eccentricity Shortest Path (MESP)} is to decide whether there exists an \emph{isometric path} $P$ in $G$ such that the distance from every vertex in the graph to its nearest vertex in $P$ is at most $R$. In this paper, we prove that MESP admits an $O(n^4)$-time algorithm on $K_{2,3}$-minor-free graphs. Our algorithm has a cubic running time when the inputs are restricted to a cactus.

cs.DS↗