Related papers: Dynamic Programming for Graphs on Surfaces
In this paper, we introduce a shallow (one-hidden-layer) physics-informed neural network for solving partial differential equations on static and evolving surfaces. For the static surface case, with the aid of level set function, the…
The dynamic scaling of distributed computations plays an important role in the utilization of elastic computational resources, such as the cloud. It enables the provisioning and de-provisioning of resources to match dynamic resource…
In this paper, a new graph partitioning problem is introduced. The depth of each part is constrained, i.e., the node count in the longest path of the corresponding sub-graph is no more than a predetermined positive integer value p. An…
Graph partitioning is a key fundamental problem in the area of big graph computation. Previous works do not consider the practical requirements when optimizing the big data analysis in real applications. In this paper, motivated by…
Graphs or networks are a very convenient way to represent data with lots of interaction. Recently, Machine Learning on Graph data has gained a lot of traction. In particular, vertex classification and missing edge detection have very…
We propose an exact algorithm for solving the longest simple path problem between two given vertices in undirected weighted graphs. By using graph partitioning and dynamic programming, we obtain an algorithm that is significantly faster…
Existing approaches for classifying dynamic graphs either lift graph kernels to the temporal domain, or use graph neural networks (GNNs). However, current baselines have scalability issues, cannot handle a changing node set, or do not take…
We improve the running time of the general algorithmic technique known as Baker's approach (1994) on H-minor-free graphs from O(n^{f(|H|)}) to O(f(|H|) n^{O(1)}). The numerous applications include e.g. a 2-approximation for coloring and…
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…
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…
Balanced partitioning is often a crucial first step in solving large-scale graph optimization problems, e.g., in some cases, a big graph can be chopped into pieces that fit on one machine to be processed independently before stitching the…
We propose a fixed-parameter tractable algorithm for the \textsc{Max-Cut} problem on embedded 1-planar graphs parameterized by the crossing number $k$ of the given embedding. A graph is called 1-planar if it can be drawn in the plane with…
An out-branching of a directed graph is a rooted spanning tree with all arcs directed outwards from the root. We consider the problem of deciding whether a given directed graph D has an out-branching with at least k leaves (Directed…
Parameterized complexity theory has lead to a wide range of algorithmic breakthroughs within the last decades, but the practicability of these methods for real-world problems is still not well understood. We investigate the practicability…
We present a practically efficient algorithm for maintaining a global minimum cut in large dynamic graphs under both edge insertions and deletions. While there has been theoretical work on this problem, our algorithm is the first…
In this paper, we show the effectiveness of a pipeline implementation of Dynamic Programming (DP) on GPU. As an example, we explain how to solve a matrix-chain multiplication (MCM) problem by DP on GPU. This problem can be sequentially…
There is an extensive literature on dynamic algorithms for a large number of graph theoretic problems, particularly for all varieties of shortest path problems. Germane to this paper are a number fully dynamic algorithms that are known for…
We present time-efficient distributed algorithms for decomposing graphs with large edge or vertex connectivity into multiple spanning or dominating trees, respectively. As their primary applications, these decompositions allow us to achieve…
The sparsest cut problem consists of identifying a small set of edges that breaks the graph into balanced sets of vertices. The normalized cut problem balances the total degree, instead of the size, of the resulting sets. Applications of…
We propose an optimal algorithm for solving the longest path problem in undirected weighted graphs. By using graph partitioning and dynamic programming, we obtain an algorithm that is significantly faster than other state-of-the-art…