Related papers: A Weight Function Lemma Heuristic for Graph Pebbli…
The cumulative pebbling complexity of a directed acyclic graph $G$ is defined as $\mathsf{cc}(G) = \min_P \sum_i |P_i|$, where the minimum is taken over all legal (parallel) black pebblings of $G$ and $|P_i|$ denotes the number of pebbles…
We present a general method for obtaining strong bounds for discrete optimization problems that is based on a concept of branching duality. It can be applied when no useful integer programming model is available, and we illustrate this with…
Graph partition is a key component to achieve workload balance and reduce job completion time in parallel graph processing systems. Among the various partition strategies, edge partition has demonstrated more promising performance in…
We propose a data-driven approach for power allocation in the context of federated learning (FL) over interference-limited wireless networks. The power policy is designed to maximize the transmitted information during the FL process under…
In graph modification problems, one is given a graph G and the goal is to apply a minimum number of modification operations (such as edge deletions) to G such that the resulting graph fulfills a certain property. For example, the Cluster…
The problem of finding the densest subgraph in a given graph has several applications in graph mining, particularly in areas like social network analysis, protein and gene analyses etc. Depending on the application, finding dense subgraphs…
When processing a batch of graphs in machine learning models such as Graph Neural Networks (GNN), it is common to combine several small graphs into one overall graph to accelerate processing and remove or reduce the overhead of padding.…
A unified framework for the Expander Mixing Lemma for irregular graphs using adjacency eigenvalues is presented, as well as two new versions of it. While the existing Expander Mixing Lemmas for irregular graphs make use of the notion of…
Many load balancing problems that arise in scientific computing applications ask to partition a graph with weights on the vertices and costs on the edges into a given number of almost equally-weighted parts such that the maximum boundary…
Let $G=(V,E,w)$ be a finite, connected graph with weighted edges. We are interested in the problem of finding a subset $W \subset V$ of vertices and weights $a_w$ such that $$ \frac{1}{|V|}\sum_{v \in V}^{}{f(v)} \sim \sum_{w \in W}{a_w…
High-performance TSP solvers like LKH search within a sparsified candidate graph rather than over all possible edges. Graph sparsification is non-trivial: keep too many edges and the solver wastes time; cut too many and it loses edges that…
Locating source of diffusion in networks is crucial for controlling and preventing epidemic risks. It has been studied under various probabilistic models. In this paper, we study source location from a deterministic point of view by…
The parametric shortest path problem is to find the shortest paths in graph where the edge costs are of the form w_ij+lambda where each w_ij is constant and lambda is a parameter that varies. The problem is to find shortest path trees for…
The mathematical model representing the equation of motion of a pendulum is nonlinear. Solutions that satisfy the equation cannot be represented by elementary functions, such as trigonometric functions. To solve such problems, it is common…
Computing maximum weight independent sets in graphs is an important NP-hard optimization problem. The problem is particularly difficult to solve in large graphs for which data reduction techniques do not work well. To be more precise,…
Let $G$ be a connected graph with vertex set $V(G)$ and edge set $E(G)$. Pebbling shift is a deletion of two pebbles from a vertex and a placement of one pebble at a neighbouring vertex. The vertex cover set, $D_{vc}$ for graph $G$ is the…
Averaging predictions of a deep ensemble of networks is apopular and effective method to improve predictive performance andcalibration in various benchmarks and Kaggle competitions. However, theruntime and training cost of deep ensembles…
Approximate solutions to various NP-hard combinatorial optimization problems have been found by learned heuristics using complex learning models. In particular, vertex (node) classification in graphs has been a helpful method towards…
A good edge-labeling (gel for short) of a graph $G$ is a function $\lambda: E(G) \to \mathbb{R}$ such that, for any ordered pair of vertices $(x, y)$ of $G$, there do not exist two distinct increasing paths from $x$ to $y$, where…
In the graph balancing problem the goal is to orient a weighted undirected graph to minimize the maximum weighted in-degree. This special case of makespan minimization is NP-hard to approximate to a factor better than 3/2 even when there…