Related papers: Theoretical analysis of git bisect
The vector-balancing problem is a fundamental problem in discrepancy theory: given T vectors in $[-1,1]^n$, find a signing $\sigma(a) \in \{\pm 1\}$ of each vector $a$ to minimize the discrepancy $\| \sum_{a} \sigma(a) \cdot a \|_{\infty}$.…
Learning graphical conditional independence structures is an important machine learning problem and a cornerstone of causal discovery. However, the accuracy and execution time of learning algorithms generally struggle to scale to problems…
We prove that for every set $S$ of vertices of a directed graph $D$, the maximum number of vertices in $S$ contained in a collection of vertex-disjoint cycles in $D$ is at least the minimum size of a set of vertices that hits all cycles…
In the \textsc{Subset Feedback Vertex Set (Subset-FVS)} problem the input is a graph $G$, a subset \(T\) of vertices of \(G\) called the `terminal' vertices, and an integer $k$. The task is to determine whether there exists a subset of…
In this paper, we investigate the problem of finding {\it bisections} (i.e., balanced bipartitions) in graphs. We prove the following two results for {\it all} graphs $G$: (1). $G$ has a bisection where each vertex $v$ has at least $(1/4 -…
Graph neural networks (GNN) have recently emerged as a vehicle for applying deep network architectures to graph and relational data. However, given the increasing size of industrial datasets, in many practical situations the message passing…
We define and study analogs of probabilistic tree embedding and tree cover for directed graphs. We define the notion of a DAG cover of a general directed graph $G$: a small collection $D_1,\dots D_g$ of DAGs so that for all pairs of…
Recently directed acyclic graph (DAG) structure learning is formulated as a constrained continuous optimization problem with continuous acyclicity constraints and was solved iteratively through subproblem optimization. To further improve…
The problem of finding an optimal vertex cover in a graph is a classic NP-complete problem, and is a special case of the hitting set question. On the other hand, the hitting set problem, when asked in the context of induced geometric…
In this paper we show that the problem of identifying an edge $(i,j)$ in a graph $G$ such that there exists an optimal vertex cover $S$ of $G$ containing exactly one of the nodes $i$ and $j$ is NP-hard. Such an edge is called a weak edge.…
Generally, a graph G, an independent set is a subset S of vertices in G such that no two vertices in S are adjacent (connected by an edge) and a vertex cover is a subset S of vertices such that each edge of G has at least one of its…
Bug reports provide critical insights into software quality, yet existing datasets often suffer from limited scope, outdated content, or insufficient metadata for machine learning. To address these limitations, we present GitBugs-a…
Stochastic gradient descent (SGD) provides a simple and efficient way to solve a broad range of machine learning problems. Here, we focus on distribution regression (DR), involving two stages of sampling: Firstly, we regress from…
Software systems evolve throughout their life cycles. Many revisions are produced over time. Model checking each revision of the software is impractical. Regression verification suggests reusing intermediate results from the previous…
Model-driven software engineering is a suitable method for dealing with the ever-increasing complexity of software development processes. Graphs and graph transformations have proven useful for representing such models and changes to them.…
Given a graph $G$ and two independent sets of same size, the Independent Set Reconfiguration Problem under token sliding ask whether one can, in a step by step manner, transform the first independent set into the second one. In each step we…
Modern version control systems such as Git or SVN include bug tracking mechanisms, through which developers can highlight the presence of bugs through bug reports, i.e., textual descriptions reporting the problem and what are the steps that…
Social network research has focused on hyperlink graphs, bibliographic citations, friend/follow patterns, influence spread, etc. Large software repositories also form a highly valuable networked artifact, usually in the form of a collection…
Algorithms for finding minimum or bounded vertex covers in graphs use a branch-and-reduce strategy, which involves exploring a highly imbalanced search tree. Prior GPU solutions assign different thread blocks to different sub-trees, while…
The MEG (minimum equivalent graph) problem is, given a directed graph, to find a small subset of the edges that maintains all reachability relations between nodes. The problem is NP-hard. This paper gives a proof that, for graphs where each…