9 papers
OmniScientist: An Omni-Modal Omni-Discipline AI Scientist
Bobo Li, Hao Fei, Tianjie Ju +2
Recent advances in foundation models have enabled AI scientists to automate increasingly complete research workflows, from hypothesis generation and code execution to manuscript pr…
On the Complexity of Hop Domination and 2-Step Domination in Graph Classes
Sandip Das, Sweta Das, Sk Samim Islam
The domination problem is a well-studied problem in graph theory. In this paper, we study two natural variants: the hop domination problem and the -step domination problem. Let…
Parameterized complexity of -Hop, -Step, and -Hop Roman Domination
Sandip Das, Sweta Das, Sk Samim Islam
The \textsc{Dominating Set} problem is a classical and extensively studied topic in graph theory and theoretical computer science. In this paper, we examine the algorithmic complex…
On the complexity of Multipacking
Sandip Das, Sk Samim Islam, Daniel Lokshtanov
A multipacking in an undirected graph is a set such that for every vertex and for every integer , the ball of radius around conta…
Multipacking on graphs and Euclidean metric space
Sk Samim Islam
A \emph{multipacking} in an undirected graph is a set such that for every vertex and for every integer , the ball of radius around…
On the Number of Almost Empty Monochromatic Triangles
Bhaswar B. Bhattacharya, Sandip Das, Sk Samim Islam +3
In this paper, we consider the problem of counting almost empty monochromatic triangles in colored planar point sets, that is, triangles whose vertices are all assigned the same co…