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At least 829 records · Page 46

Graph-based Simulation Framework for Power Resilience Estimation and Enhancement

The increasing frequency of extreme weather events poses significant risks to power distribution systems, leading to widespread outages and severe economic and social consequences. This paper presents a novel simulation framework for assessing and enhancing the resilience of power distribution networks under such conditions. Resilience is estimated through Monte Carlo simulations, which simulate extreme weather scenarios and evaluate the impact on infrastructure fragility. Due to the proprietary nature of power network topology, a distribution network is synthesized using publicly available data. To generate the weather scenarios, an extreme weather generation method is developed. To enhance resilience, renewable resources such as solar panels and energy storage systems (batteries in this study) are incorporated. A customized Genetic Algorithm is proposed to determine the optimal locations and capacities for solar panels and battery installations, maximizing resilience while balancing cost constraints. Experiment results demonstrate that on a large-scale synthetic distribution network with more than 300,000 nodes and 300,000 edges, the proposed framework can efficiently evaluate the resilience, and enhance the resilience through the installations of distributed energy resources (DERs), providing utilities with valuable insights for community-level power system resilience estimation and enhancement.

Wang, Xuesong [Wayne State Univ., Detroit, MI (Uni↗

Vectorization of Dynamic Subgraphs via Generative Models (Final Report)

An important class of data analysis tasks stem from comparing subsets of connected records within massive sets of complex relational data. A common approach is to represent each set of connected records with a small graph, or set of data entities (graph vertices) and their relationships (graph edges), and efficient methods to gauge similarity for pairs of graphs are of high interest. This project concentrated on dynamic graphs, where each edge record has an associated timestamp denoting the time of observation. Pre-existing techniques for comparing dynamic graphs concentrate on either computing graph edit distance (number of vertex and edge deletion, addition, and timestamp modifications) or vectorizing the graph with counts of a limited set of dynamic graph motifs (tiny fundamental subgraphs) and computing distances between the vectors. These approaches are less able to see similarities in graphs that are fairly different in size but come from identical graph generation processes. The motif counting approach can be improved for graphs from the same process, but suffers from requiring many types of motifs meaning it is expensive. Moreover, many motifs are not present for small graphs, meaning realizing a a much larger graph came from the same process is difficult.

97 MATHEMATICS AND COMPUTING↗

TripleGraph

RDF triplestores are great tools for online graph analytic processing (i.e., graph pattern query processing), but they do not provide graph mining capabilities (e.g., PageRank, connected-component analysis, node eccentricity, etc.). The software title “TripleGraph” is a graph analysis toolkit, which uses an RDF triplestore as its backend for creating, manipulating, mining, and programming with large scale property graphs. It allows users to run various graph mining algorithms easily. User can import edgelist-formatted (homogeneous graph) or JSON-formatted graph (property graph) into the RDF triplestore using the provided tool and perform various analysis such as (1) Node/edge retrieval and manipulation, (2) Pathfinding between two given nodes, (3) Running graph mining algorithms (PageRank/Personalized PageRank, Single Source Shortest Path/Multi-Source Shortest Path, Connected Component, Node Eccentricity, Peer Pressure Clustering). It supports standard graph data format and works with a standard SPARQL endpoint like Jena Fuseki. It allows users to perform online graph analytic processing and graph mining on the same platform (a triplestore).

Sangkeun, MattLee↗

Diffusion Codes: Self-Correction from Small(er)-Set Expansion with Tunable Non-locality

Optimal constructions of classical LDPC codes can be obtained by choosing the Tanner graph uniformly at random among biregular graphs. We introduce a class of codes that we call ``diffusion codes'', defined by placing each edge connecting bits and checks on some graph, and acting on that graph with a random SWAP network. By tuning the depth of the SWAP network, we can tune a tradeoff between the amount of randomness -- and hence the optimality of code parameters -- and locality with respect to the underlying graph. For diffusion codes defined on the cycle graph, if the SWAP network has depth $\sim Tn$ with $T> n^{2β}$ for arbitrary $β>0$, then we prove that almost surely the Tanner graph is a lossless ``smaller set'' vertex expander for small sets up size $δ\sim \sqrt T \sim n^β$, with bounded bit and check degree. At the same time, the geometric size of the largest stabilizer is bounded by $\sqrt T$ in graph distance. We argue, based on physical intuition, that this result should hold more generally on arbitrary graphs. By taking hypergraph products of these classical codes we obtain quantum LDPC codes defined on the torus with smaller-set boundary and co-boundary expansion and the same expansion/locality tradeoffs as for the classical codes. These codes are self-correcting and admit single-shot decoding, while having the geometric size of the stabilizer growing as an arbitrarily small power law. Our proof technique establishes mixing of a random SWAP network on small subsystems at times scaling with only the subsystem size, which may be of independent interest.

Combinatorics (math.CO)↗

Streaming Matching and Edge Cover in Practice

Graph algorithms with polynomial space and time requirements often become infeasible for massive graphs with billions of edges or more. State-of-the-art approaches therefore employ approximate serial, parallel, and distributed algorithms to tackle these challenges. However, such approaches require storing the entire graph in memory and thus need access to costly computing resources such as clusters and supercomputers. In this paper, we present practical streaming approaches for solving massive graph problems using limited memory for two prototypical graph problems: maximum weighted matching and minimum weighted edge cover. For matching, we conduct a thorough computational study on two of the semi-streaming algorithms including a recent breakthrough result that achieves a $1/(2+\varepsilon)$-approximation of the weight while using $O( n \log W /\epsilon)$ memory (here $n$ is the number of vertices and $W$ is the maximum edge weight), designed by Paz and Schwartzman [SODA, 2017]. Empirically, we show that the semi-streaming algorithms produce matchings whose weight is close to the best $1/2$-approximate offline algorithm while requiring less time and an order-of-magnitude less memory. For minimum weighted edge cover, we develop three novel semi-streaming algorithms. Two of these algorithms require a single pass through the input graph, require $O(n \log n)$ memory, and provide a 2-approximation guarantee on the objective. We also leverage a relationship between approximate maximum weighted matching and approximate minimum weighted edge cover to develop a two-pass $3/2+\epsilon$-approximate algorithm with the memory requirement of Paz and Schwartzman's semi-streaming matching algorithm. These streaming approaches are compared against the state-of-the-art 3/2-approximate offline algorithm. The semi-streaming matching and the novel edge cover algorithms proposed in this paper can process graphs with several billions of edges in under 30 minutes using 6 GB of memory, which is at least an order of magnitude improvement from the offline (non-streaming) algorithms. For the largest graph, the best alternative offline parallel approximation algorithm (GPA+ROMA) could not finish in three hours even while employing hundreds of processors and 1 TB of memory. We also demonstrate an application of the semi-streaming algorithm by computing a matching using linearly bounded memory on item intersection graphs derived from three machine learning datasets, whereas the existing offline algorithms could not complete on one of these datasets since their memory requirements exceeded 1TB.

Ferdous, S M.↗

GraMeR: Gra ph Me ta R einforcement learning for multi-objective influence maximization

Influence maximization (IM) is a combinatorial problem of identifying a subset of seed nodes in a network (graph), which when activated, provide a maximal spread of influence in the network for a given diffusion model and a budget for seed set size. IM has numerous applications such as viral marketing, epidemic control, sensor placement and other network-related tasks. However, its practical uses are limited due to the computational complexity of current algorithms. Recently, deep reinforcement learning has been leveraged to solve IM in order to ease the computational burden. However, there are serious limitations in current approaches, including narrow IM formulation that only consider influence via spread and ignore self-activation, low scalability to large graphs, and lack of generalizability across graph families leading to a large running time for every test network. In this work, we address these limitations through a unique approach that involves: (1) Formulating a generic IM problem as a Markov decision process that handles both intrinsic and influence activations; (2)incorporating generalizability via meta-learning across graph families. There are previous works that combine deep reinforcement learning with graph neural network, but this work solves a more realistic IM problem and incorporates generalizability across graphs via meta reinforcement learning. Extensive experiments are carried out in various standard networks to validate performance of the proposed Graph Meta Reinforcement learning (GraMeR) framework. Finally, the results indicate that GraMeR is multiple orders faster and generic than conventional approaches when applied on small to medium scale graphs.

97 MATHEMATICS AND COMPUTING↗

An automated integrated web-based smart tool for open stope design

The Stability Graph is a widely used tool for the design of open stopes in underground mining. Many users of the Stability Graph still apply this design method manually. Although the manual approach has benefits, using multiple graphs and stability number computation charts for each stope surface is time-consuming, even for the experienced mining engineer. Current practice in the use of the method also limits data sharing. This paper presents a StopeSoft web-based tool for open stope stability prediction that is developed on the basis of the Stability Graph method and is available at openstope.com. StopeSoft incorporates flexibility in terms of Stability Graph options and incorporates additional critical factors often overlooked. As a web-based tool, StopeSoft encourages and makes data sharing possible globally, focused on expanding the database and improving the current limitations of the Stability Graph to provide practical, reliable solutions for mining engineers, consultants, and academics. The StopeSoft automated process facilitates the process of open stope stability prediction, saving time and minimizing potential human errors. Statistical treatment of the data accounts for the variability of input parameters to emphasize the probabilistic nature of the Stability Graph method. The probabilistic interpretation of the stability states of stope surfaces eliminates the false feeling of absolute stope performance based on its location on the Stability Graph , as implied by the deterministic approach.

58 GEOSCIENCES↗

Hypergraph Models of Biological Networks to Identify Genes Critical to Pathogenic Viral Response

Motivation: Representing biological networks as graphs is a powerful approach to reveal underlying patterns, signatures, and critical components from high-throughput biomolecular data. However, graphs do not natively capture the multi-way relationships present among genes and proteins in biological systems such as protein complexes, metabolic reactions, and signal transduction pathways. Hypergraphs are generalizations of graphs that naturally model multi-way interactions in data, and we therefore seek to understand how they can more faithfully identify, and potentially predict, complex relationships in genomic expression data sets. Results: We compiled a novel data set of transcriptional host response to pathogenic viral infections and formulated relationships between genes as a hypergraph where hyperedges are differentially expressed genes and vertices represent conditions. We find that hypergraph betweenness centrality is a superior method for identification of genes important to viral response when compared with graph centrality. Our results demonstrate the utility of using hypergraphs to represent complex biological systems, and highlight potentially interesting biological results about host response to highly pathogenic viruses.

systems biology, hypergraph, viral infection, biol↗

4-Clique network minor embedding for quantum annealers

Quantum annealing is a quantum algorithm for computing solutions to combinatorial optimization problems. This study proposes a method for minor embedding optimization problems onto sparse quantum annealing hardware graphs called 4-clique network minor embedding. This method is in contrast to the standard minor embedding technique of using a path of linearly connected qubits in order to represent a logical variable state. The 4-clique minor embedding is possible on Pegasus graph connectivity, which is the native hardware graph for some of the current D-Wave quantum annealers. The Pegasus hardware graph contains many cliques of size 4, making it possible to form a graph composed entirely of paths of connected 4-cliques on which a problem can be minor-embedded. The 4-clique chains come at the cost of additional qubit usage on the hardware graph, but they allow for stronger coupling within each chain, thereby increasing chain integrity, reducing chain breaks, and allow for greater usage of the available energy scale for programming logical problem coefficients on current quantum annealers. The 4-clique minor embedding technique is compared with the standard linear path minor embedding with experiments on two D-Wave quantum annealing processors with Pegasus hardware graphs. We show proof-of-concept experiments where the 4-clique minor embeddings can use weak chain strengths while successfully carrying out the computation of minimizing random all-to-all spin glass problem instances. Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗