Related papers: Visibility Polygons and Visibility Graphs among Dy…
An ortho-polygon visibility representation $\Gamma$ of a $1$-plane graph $G$ (OPVR of $G$) is an embedding preserving drawing that maps each vertex of $G$ to a distinct orthogonal polygon and each edge of $G$ to a vertical or horizontal…
We present an algorithm to solve a system of diagonal polynomial equations over finite fields when the number of variables is greater than some fixed polynomial of the number of equations whose degree depends only on the degree of the…
We present an algorithm to support the dynamic embedding in the plane of a dynamic graph. An edge can be inserted across a face between two vertices on the face boundary (we call such a vertex pair linkable), and edges can be deleted. The…
This paper introduces a novel $k$-cell decomposition method for pursuit-evasion problems in polygonal environments, where a searcher is equipped with a $k$-modem: a device capable of seeing through up to $k$ walls. The proposed…
We show an algorithm for dynamic maintenance of connectivity information in an undirected planar graph subject to edge deletions. Our algorithm may answer connectivity queries of the form `Are vertices $u$ and $v$ connected with a path?' in…
We study dynamic algorithms in the model of algorithms with predictions. We assume the algorithm is given imperfect predictions regarding future updates, and we ask how such predictions can be used to improve the running time. This can be…
Geometric data augmentation is widely used in segmentation workflows, but polygon annotations are often assumed to remain valid after transformation. This assumption can fail in structured domains such as architectural floorplan analysis,…
Fully dynamic graph is a data structure that (1) supports edge insertions and deletions and (2) answers problem specific queries. The time complexity of (1) and (2) are referred to as the update time and the query time respectively. There…
Many algorithms which exactly solve hard problems require branching on more or less complex structures in order to do their job. Those who design such algorithms often find themselves doing a meticulous analysis of numerous different cases…
We propose a fully dynamic algorithm for maintaining reachability information in directed graphs. The proposed deterministic dynamic algorithm has an update time of $O((ins*n^{2}) + (del * (m+n*log(n))))$ where $m$ is the current number of…
Computing a dense subgraph is a fundamental problem in graph mining, with a diverse set of applications ranging from electronic commerce to community detection in social networks. In many of these applications, the underlying context is…
Viewpoint planning is critical for efficient 3D data acquisition in applications such as 3D reconstruction, building life-cycle management, navigation, and interior decoration. However, existing methods often neglect key optimization…
A rectangle visibility representation (RVR) of a graph consists of an assignment of axis-aligned rectangles to vertices such that for every edge there exists a horizontal or vertical line of sight between the rectangles assigned to its…
A point visibility graph is a graph induced by a set of points in the plane, where every vertex corresponds to a point, and two vertices are adjacent whenever the two corresponding points are visible from each other, that is, the open…
We study terrain visibility graphs, a well-known graph class closely related to polygon visibility graphs in computational geometry, for which a precise graph-theoretical characterization is still unknown. Over the last decade, terrain…
In this paper we present the first deterministic polynomial time algorithm for determining the existence of a Hamiltonian cycle and finding a Hamiltonian cycle in general graphs. Our algorithm can also solve the Hamiltonian path problem in…
Differentially private algorithms protect individuals in data analysis scenarios by ensuring that there is only a weak correlation between the existence of the user in the data and the result of the analysis. Dynamic graph algorithms…
In the recent research of data mining, frequent structures in a sequence of graphs have been studied intensively, and one of the main concern is changing structures along a sequence of graphs that can capture dynamic properties of data. On…
While many graph drawing algorithms consider nodes as points, graph visualization tools often represent them as shapes. These shapes support the display of information such as labels or encode various data with size or color. However, they…
We propose a hybrid image-space/object-space solution to the classical hidden surface removal problem: Given n disjoint triangles in Real^3 and p sample points (``pixels'') in the xy-plane, determine the first triangle directly behind each…