相关论文: chipfiring: A Python Package for Efficient Mathema…

The dollar game is a chip-firing game introduced by Baker and Norine (2007) as a context in which to formulate and prove the Riemann-Roch theorem for graphs. A divisor on a graph is a formal integer sum of vertices. Each determines a dollar…

We extend the notion of chip-firing to weighted graphs, and generalize the Greedy Algorithm and Dhar's Burning Algorithm to weighted graphs. For a vertex $q \in V(\Gamma)$, we give an upper bound for the number of linearly equivalent…

Baker and Norine introduced a graph-theoretic analogue of the Riemann-Roch theory. A central notion in this theory is the rank of a divisor. In this paper we prove that computing the rank of a divisor on a graph is NP-hard. The…

We study the interplay between chip-firing games and potential theory on graphs, characterizing reduced divisors ($G$-parking functions) on graphs as the solution to an energy (or potential) minimization problem and providing an algorithm…

Chip-firing is a combinatorial game played on a graph in which we place and disperse chips on vertices until a stable state is reached. We study a chip-firing variant played on an infinite rooted directed $k$-ary tree, where we place…

Graph Partitioning is widely used in many real-world applications such as fraud detection and social network analysis, in order to enable the distributed graph computing on large graphs. However, existing works fail to balance the…

LiteEFG is an efficient library with easy-to-use Python bindings, which can solve multiplayer extensive-form games (EFGs). LiteEFG enables the user to express computation graphs in Python to define updates on the game tree structure. The…

Chip-firing is a combinatorial game played on an undirected graph in which we place chips on vertices. We study chip-firing on an infinite binary tree in which we add a self-loop to the root to ensure each vertex has degree 3. A vertex can…

In his preprint https://arxiv.org/abs/1308.3813, Cartwright introduced the notion of a weak tropical complex in order to generalize the concepts of divisors and the Picard group on graphs from Baker and Norine's paper Riemann-Roch and…

In this paper, we present "Graph Feature Preprocessor", a software library for detecting typical money laundering patterns in financial transaction graphs in real time. These patterns are used to produce a rich set of transaction features…

Graph representations of programs are commonly a central element of machine learning for code research. We introduce an open source Python library python_graphs that applies static analysis to construct graph representations of Python…

This paper describes the design and use of the graph-based parsing framework and toolkit UniParse, released as an open-source python software package. UniParse as a framework novelly streamlines research prototyping, development and…

The Graph Burning Problem (GBP) is a combinatorial optimization problem that has gained relevance as a tool for quantifying a graph's vulnerability to contagion. Although it is based on a very simple propagation model, its decision version…

Sampling graphs is an important task in data mining. In this paper, we describe Little Ball of Fur a Python library that includes more than twenty graph sampling algorithms. Our goal is to make node, edge, and exploration-based network…

Partitioning a graph into blocks of "roughly equal" weight while cutting only few edges is a fundamental problem in computer science with a wide range of applications. In particular, the problem is a building block in applications that…

We investigate Riemann-Roch theory for directed graphs. The Riemann-Roch criteria of Amini and Manjunath is generalized to all integer lattices orthogonal to some positive vector. Using generalized notions of a $v_0$-reduced divisor and…

We introduce pygrank, an open source Python package to define, run and evaluate node ranking algorithms. We provide object-oriented and extensively unit-tested algorithm components, such as graph filters, post-processors, measures,…

This paper provides a friendly introduction to chip-firing games and graph gonality. We use graphs coming from the five Platonic solids to illustrate different tools and techniques for studying these games, including independent sets,…

We introduce milearn, a Python package for multi-instance learning (MIL) that follows the familiar scikit-learn fit/predict interface while providing a unified framework for both classical and neural-network-based MIL algorithms for…

Chip firing provides a way to study the sandpile group (also known as the Jacobian) of a graph. We use a generalized version of chip firing to bound the number of invariant factors of the critical group of an arithmetical structure on a…