相关论文: Simultaneous FPQ-Ordering and Hybrid Planarity Tes…
The problem Simultaneous Embedding with Fixed Edges (SEFE) asks for two planar graph $G^1 = (V^1, E^1)$ and $G^2 = (V^2, E^2)$ sharing a common subgraph $G = G^1 \cap G^2$ whether they admit planar drawings such that the common graph is…
A graph is near-planar if it can be obtained from a planar graph by adding an edge. We show the surprising fact that it is NP-hard to compute the crossing number of near-planar graphs. A graph is 1-planar if it has a drawing where every…
A k-page book embedding of a graph G draws the vertices of G on a line and the edges on k half-planes (called pages) bounded by this line, such that no two edges on the same page cross. We study the problem of determining whether G admits a…
We consider constrained variants of graph homomorphisms such as embeddings, monomorphisms, full homomorphisms, surjective homomorpshims, and locally constrained homomorphisms. We also introduce a new variation on this theme which derives…
We study dynamic planar graphs with $n$ vertices, subject to edge deletion, edge contraction, edge insertion across a face, and the splitting of a vertex in specified corners. We dynamically maintain a combinatorial embedding of such a…
In many applied sciences a popular analysis strategy for high-dimensional data is to fit many multivariate generalized linear models in parallel. This paper presents a novel approach to address the resulting multiple testing problem by…
We consider mixed-integer quadratic optimization problems with banded matrices and indicator variables. These problems arise pervasively in statistical inference problems with time-series data, where the banded matrix captures the temporal…
Federated learning enables training on a massive number of edge devices. To improve flexibility and scalability, we propose a new asynchronous federated optimization algorithm. We prove that the proposed approach has near-linear convergence…
This paper introduces a problem in which the state of a system needs to be determined through costly tests of its components by a limited number of testing units and before a given deadline. We also consider a closely related search problem…
Simultaneous embedding is concerned with simultaneously representing a series of graphs sharing some or all vertices. This forms the basis for the visualization of dynamic graphs and thus is an important field of research. Recently there…
Many variations of the classical graph coloring model have been intensively studied due to their multiple applications; scheduling problems and aircraft assignments, for instance, motivate the robust coloring problem. This model gets to…
In this article, we study parameterized complexity theory from the perspective of logic, or more specifically, descriptive complexity theory. We propose to consider parameterized model-checking problems for various fragments of first-order…
List colouring is an NP-complete decision problem even if the total number of colours is three. It is hard even on planar bipartite graphs. We give a polynomial-time algorithm for solving list colouring of permutation graphs with a bounded…
Consider a graph drawn on a surface (for example, the plane minus a finite set of obstacle points), possibly with crossings. We provide an algorithm to decide whether such a drawing can be untangled, namely, if one can slide the vertices…
Using Landau-de Gennes theory to describe nematic order, we study a frustrated cell consisting of nematic liquid crystal confined between two parallel plates. We prove the uniqueness of equilibrium states for a small cell width. Letting the…
A drawing in the plane ($\mathbb{R}^2$) of a graph $G=(V,E)$ equipped with a function $\gamma: V \rightarrow \mathbb{N}$ is \emph{$x$-bounded} if (i) $x(u) <x(v)$ whenever $\gamma(u)<\gamma(v)$ and (ii) $\gamma(u)\leq\gamma(w)\leq…
This paper proposes a control algorithm for stable implementation of asynchronous parallel quadratic programming (PQP) through dual decomposition technique. In general, distributed and parallel optimization requires synchronization of data…
We investigate the query evaluation problem for fixed queries over fully dynamic databases where tuples can be inserted or deleted. The task is to design a dynamic data structure that can immediately report the new result of a fixed query…
In this study, we investigate a robust single-machine scheduling problem under processing time uncertainty. The uncertainty is modeled using the budgeted approach, where each job has a nominal and deviation processing time, and the number…
We prove the #P-hardness of the counting problems associated with various satisfiability, graph and combinatorial problems, when restricted to planar instances. These problems include \begin{romannum} \item[{}] {\sc 3Sat, 1-3Sat, 1-Ex3Sat,…