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We introduce a variation of the scheduling with precedence constraints problem that has applications to molecular folding and production management. We are given a bipartite graph $H=(B,S)$. Vertices in $B$ are thought of as goods or…
In this paper, we begin the exploration of vertex-ordering problems through the lens of exponential-time approximation algorithms. In particular, we ask the following question: Can we simultaneously beat the running times of the fastest…
Many graph problems can be solved using ordered parallel graph algorithms that achieve significant speedup over their unordered counterparts by reducing redundant work. This paper introduces a new priority-based extension to GraphIt, a…
Backtracking search algorithms are often used to solve the Constraint Satisfaction Problem (CSP). The efficiency of backtracking search depends greatly on the variable ordering heuristics. Currently, the most commonly used heuristics are…
A highly successful approach to route planning in networks (particularly road networks) is to identify a hierarchy in the network that allows faster queries after some preprocessing that basically inserts additional "shortcut"-edges into a…
The paper focuses on two problems: (i) how to orient the edges of an undirected graph in order to maximize the number of ordered vertex pairs (x,y) such that there is a directed path from x to y, and (ii) how to orient the edges so as to…
We propose a heuristic method that generates a graph for order/degree problem. Target graphs of our heuristics have large order (> 4000) and diameter 3. We describe the ob- servation of smaller graphs and basic structure of our heuristics.…
The graph coloring problem asks for an assignment of the minimum number of distinct colors to vertices in an undirected graph with the constraint that no pair of adjacent vertices share the same color. The problem is a thoroughly studied…
The most commonly used method to tackle the graph partitioning problem in practice is the multilevel approach. During a coarsening phase, a multilevel graph partitioning algorithm reduces the graph size by iteratively contracting nodes and…
Graphs are often used to model relationships between entities. The identification and visualization of clusters in graphs enable insight discovery in many application areas, such as life sciences and social sciences. Force-directed graph…
Graph neural networks (GNNs) are a type of neural network capable of learning on graph-structured data. However, training GNNs on large-scale graphs is challenging due to iterative aggregations of high-dimensional features from neighboring…
A scalable graphical method is presented for selecting, and partitioning datasets for the training phase of a classification task. For the heuristic, a clustering algorithm is required to get its computation cost in a reasonable proportion…
Graph analytics attract much attention from both research and industry communities. Due to the linear time complexity, the $k$-core decomposition is widely used in many real-world applications such as biology, social networks, community…
The algorithmic differentiation (AD) of mathematical functions can be interpreted as a sequence of vertex eliminations in an underlying directed acyclic graph. The problem of determining a minimum-cost elimination ordering, which we call…
Big graphs (networks) arising in numerous application areas pose significant challenges for graph analysts as these graphs grow to billions of nodes and edges and are prohibitively large to fit in the main memory. Finding the number of…
Graphlets of order $k$ in a graph $G$ are connected subgraphs induced by $k$ nodes (called $k$-graphlets) or by $k$ edges (called edge $k$-graphlets). They are among the interesting subgraphs in network analysis to get insights on both the…
In the classical facility location problem we consider a graph $G$ with fixed weights on the edges of $G$. The goal is then to find an optimal positioning for a set of facilities on the graph with respect to some objective function. We…
We consider the task of drawing a graph on multiple horizontal layers, where each node is assigned a layer, and each edge connects nodes of different layers. Known algorithms determine the orders of nodes on each layer to minimize crossings…
The crossing resolution of a non-planar drawing of a graph is the value of the minimum angle formed by any pair of crossing edges. Recent experiments have shown that the larger the crossing resolution is, the easier it is to read and…
We consider directed graph algorithms in a streaming setting, focusing on problems concerning orderings of the vertices. This includes such fundamental problems as topological sorting and acyclicity testing. We also study the related…