Papers by Heather Guarnera
arXiv (Cornell University), Jul 28, 2020
A graph is Helly if its disks satisfy the Helly property, i.e., every family of pairwise intersec... more A graph is Helly if its disks satisfy the Helly property, i.e., every family of pairwise intersecting disks in G has a common intersection. It is known that for every graph G, there exists a unique smallest Helly graph H(G) into which G isometrically embeds; H(G) is called the injective hull of G. Motivated by this, we investigate the structural properties of the injective hulls of various graph classes. We say that a class of graphs C is closed under Hellification if G ∈ C implies H(G) ∈ C. We identify several graph classes that are closed under Hellification. We show that permutation graphs are not closed under Hellification, but chordal graphs, squarechordal graphs, and distance-hereditary graphs are. Graphs that have an efficiently computable injective hull are of particular interest. A linear-time algorithm to construct the injective hull of any distance-hereditary graph is provided and we show that the injective hull of several graphs from some other well-known classes of graphs are impossible to compute in subexponential time. In particular, there are split graphs, cocomparability graphs, bipartite graphs G such that H(G) contains Ω(a n) vertices, where n = |V (G)| and a > 1.
arXiv (Cornell University), May 4, 2020
A new metric parameter for a graph, Helly-gap, is introduced. A graph G is called α-weakly-Helly ... more A new metric parameter for a graph, Helly-gap, is introduced. A graph G is called α-weakly-Helly if any system of pairwise intersecting disks in G has a nonempty common intersection when the radius of each disk is increased by an additive value α. The minimum α for which a graph G is α-weakly-Helly is called the Helly-gap of G and denoted by α(G). The Helly-gap of a graph G is characterized by distances in the injective hull H(G), which is a (unique) minimal Helly graph which contains G as an isometric subgraph. This characterization is used as a tool to generalize many eccentricity related results known for Helly graphs (α(G) = 0), as well as for chordal graphs (α(G) ≤ 1), distance-hereditary graphs (α(G) ≤ 1) and δ-hyperbolic graphs (α(G) ≤ 2δ), to all graphs, parameterized by their Helly-gap α(G). Several additional graph classes are shown to have a bounded Helly-gap, including AT-free graphs and graphs with bounded tree-length, bounded chordality or bounded α i-metric.
Springer eBooks, 2021
A graph is Helly if every family of pairwise intersecting balls has a nonempty common intersectio... more A graph is Helly if every family of pairwise intersecting balls has a nonempty common intersection. The class of Helly graphs is the discrete analogue of the class of hyperconvex metric spaces. It is also known that every graph isometrically embeds into a Helly graph, making the latter an important class of graphs in Metric Graph Theory. We study diameter, radius and all eccentricity computations within the Helly graphs. Under plausible complexity assumptions, neither the diameter nor the radius can be computed in truly subquadratic time on general graphs. In contrast to these negative results, it was recently shown that the radius and the diameter of an n-vertex m-edge Helly graph G can be computed with high probability inÕ(m √ n) time (i.e., subquadratic in n+m). In this paper, we improve that result by presenting a deterministic O(m √ n) time algorithm which computes not only the radius and the diameter but also all vertex eccentricities in a Helly graph. Furthermore, we give a parameterized linear-time algorithm for this problem on Helly graphs, with the parameter being the Gromov hyperbolicity δ. More specifically, we show that the radius and a central vertex of an m-edge δ-hyperbolic Helly graph G can be computed in O(δm) time and that all vertex eccentricities in G can be computed in O(δ 2 m) time. To show this more general result, we heavily use our new structural properties obtained for Helly graphs.
Journal of Computer and System Sciences, Sep 1, 2020
A graph G = (V, E) is δ-hyperbolic if for any four vertices u, v, w, x, the two larger of the thr... more A graph G = (V, E) is δ-hyperbolic if for any four vertices u, v, w, x, the two larger of the three distance sums d(u, v) + d(w, x), d(u, w) + d(v, x), d(u, x) + d(v, w) differ by at most 2δ ≥ 0. This paper describes the eccentricity terrain of a δ-hyperbolic graph. The eccentricity function e G (v) = max{d(v, u) : u ∈ V } partitions vertices of G into eccentricity layers C k (G) = {v ∈ V : e G (v) = rad(G) + k}, k ∈ N, where rad(G) = min{e G (v) : v ∈ V } is the radius of G. The paper studies the eccentricity layers of vertices along shortest paths, identifying such terrain features as hills, plains, valleys, terraces, and plateaus. It introduces the notion of β-pseudoconvexity, which implies Gromov's-quasiconvexity, and illustrates the abundance of pseudoconvex sets in δ-hyperbolic graphs. It shows that all sets C ≤k (G) = {v ∈ V : e G (v) ≤ rad(G) + k}, k ∈ N, are (2δ − 1)-pseudoconvex. Several bounds on the eccentricity of a vertex are obtained which yield a few approaches to efficiently approximating all eccentricities.
Detection of Named Branch Origin for Git Commits
The named branch on which a change is committed in a Git repository provides valuable insight int... more The named branch on which a change is committed in a Git repository provides valuable insight into the evolution of a software project, including a natural and logical ordering of commits categorized by the developer at the time of the change. In addition, the name of the branch provides semantic context as to the nature of the changes along that branch. However, this branch name is unrecorded in the historical archive of Git repositories. In this thesis, a heuristics-based algorithm is presented to detect the named branch origin of commits based on the merge commit messages. An empirical evaluation shows precision levels reaching an average of 87% as seen when applied to generated test repositories and an average recall of over 97% when applied to generated test repositories and forty-four open source systems. This is shown to constitute an enormous increase in recall when compared to the only existing algorithm for branch name detection. Additionally, a detailed explanation of common merge commit messages, merge types, and branch names as found in over forty open-source projects is discussed.
Theoretical Computer Science, Sep 1, 2020
A graph G = (V, E) is distance hereditary if every induced path of G is a shortest path. In this ... more A graph G = (V, E) is distance hereditary if every induced path of G is a shortest path. In this paper, we show that the eccentricity function e(v) = max{d(v, u) : u ∈ V } in any distance-hereditary graph G is almost unimodal, that is, every vertex v with e(v) > rad(G) + 1 has a neighbor with smaller eccentricity. Here, rad(G) = min{e(v) : v ∈ V } is the radius of graph G. Moreover, we use this result to fully characterize the centers of distance-hereditary graphs. Several bounds on the eccentricity of a vertex with respect to its distance to the center of G or to the ends of a diametral path are established. Finally, we propose a new linear time algorithm to compute all eccentricities in a distance-hereditary graph.
Graphs and Combinatorics
A graph is Helly if its disks satisfy the Helly property, i.e., every family of pairwise intersec... more A graph is Helly if its disks satisfy the Helly property, i.e., every family of pairwise intersecting disks in G has a common intersection. It is known that for every graph G, there exists a unique smallest Helly graph H(G) into which G isometrically embeds; H(G) is called the injective hull of G. Motivated by this, we investigate the structural properties of the injective hulls of various graph classes. We say that a class of graphs C is closed under Hellification if G ∈ C implies H(G) ∈ C. We identify several graph classes that are closed under Hellification. We show that permutation graphs are not closed under Hellification, but chordal graphs, squarechordal graphs, and distance-hereditary graphs are. Graphs that have an efficiently computable injective hull are of particular interest. A linear-time algorithm to construct the injective hull of any distance-hereditary graph is provided and we show that the injective hull of several graphs from some other well-known classes of graphs are impossible to compute in subexponential time. In particular, there are split graphs, cocomparability graphs, bipartite graphs G such that H(G) contains Ω(a n) vertices, where n = |V (G)| and a > 1.
arXiv (Cornell University), Nov 22, 2019
A graph G = (V, E) is distance hereditary if every induced path of G is a shortest path. In this ... more A graph G = (V, E) is distance hereditary if every induced path of G is a shortest path. In this paper, we show that the eccentricity function e(v) = max{d(v, u) : u ∈ V } in any distance-hereditary graph G is almost unimodal, that is, every vertex v with e(v) > rad(G) + 1 has a neighbor with smaller eccentricity. Here, rad(G) = min{e(v) : v ∈ V } is the radius of graph G. Moreover, we use this result to fully characterize the centers of distance-hereditary graphs. Several bounds on the eccentricity of a vertex with respect to its distance to the center of G or to the ends of a diametral path are established. Finally, we propose a new linear time algorithm to compute all eccentricities in a distance-hereditary graph.
Lecture Notes in Computer Science, 2021
A graph is Helly if every family of pairwise intersecting balls has a nonempty common intersectio... more A graph is Helly if every family of pairwise intersecting balls has a nonempty common intersection. The class of Helly graphs is the discrete analogue of the class of hyperconvex metric spaces. It is also known that every graph isometrically embeds into a Helly graph, making the latter an important class of graphs in Metric Graph Theory. We study diameter, radius and all eccentricity computations within the Helly graphs. Under plausible complexity assumptions, neither the diameter nor the radius can be computed in truly subquadratic time on general graphs. In contrast to these negative results, it was recently shown that the radius and the diameter of an n-vertex m-edge Helly graph G can be computed with high probability inÕ(m √ n) time (i.e., subquadratic in n + m). In this paper, we improve that result by presenting a deterministic O(m √ n) time algorithm which computes not only the radius and the diameter but also all vertex eccentricities in a Helly graph. Furthermore, we give a parameterized linear-time algorithm for this problem on Helly graphs, with the parameter being the Gromov hyperbolicity δ. More specifically, we show that the radius and a central vertex of an m-edge δ-hyperbolic Helly graph G can be computed in O(δm) time and that all vertex eccentricities in G can be computed in O(δ 2 m) time. To show this more general result, we heavily use our new structural properties obtained for Helly graphs.
Fellow Travelers Phenomenon Present in Real-World Networks
Complex Networks & Their Applications X, 2022
Theoretical Computer Science, 2021
A new metric parameter for a graph, Helly-gap, is introduced. A graph G is called α-weakly-Helly ... more A new metric parameter for a graph, Helly-gap, is introduced. A graph G is called α-weakly-Helly if any system of pairwise intersecting disks in G has a nonempty common intersection when the radius of each disk is increased by an additive value α. The minimum α for which a graph G is α-weakly-Helly is called the Helly-gap of G and denoted by α(G). The Helly-gap of a graph G is characterized by distances in the injective hull H(G), which is a (unique) minimal Helly graph which contains G as an isometric subgraph. This characterization is used as a tool to generalize many eccentricity related results known for Helly graphs (α(G) = 0), as well as for chordal graphs (α(G) ≤ 1), distance-hereditary graphs (α(G) ≤ 1) and δ-hyperbolic graphs (α(G) ≤ 2δ), to all graphs, parameterized by their Helly-gap α(G). Several additional graph classes are shown to have a bounded Helly-gap, including AT-free graphs and graphs with bounded tree-length, bounded chordality or bounded α i-metric.
Theoretical Computer Science, 2020
A graph G = (V, E) is distance hereditary if every induced path of G is a shortest path. In this ... more A graph G = (V, E) is distance hereditary if every induced path of G is a shortest path. In this paper, we show that the eccentricity function e(v) = max{d(v, u) : u ∈ V } in any distance-hereditary graph G is almost unimodal, that is, every vertex v with e(v) > rad(G) + 1 has a neighbor with smaller eccentricity. Here, rad(G) = min{e(v) : v ∈ V } is the radius of graph G. Moreover, we use this result to fully characterize the centers of distance-hereditary graphs. Several bounds on the eccentricity of a vertex with respect to its distance to the center of G or to the ends of a diametral path are established. Finally, we propose a new linear time algorithm to compute all eccentricities in a distance-hereditary graph.
Journal of Computer and System Sciences, 2020
A graph G = (V, E) is δ-hyperbolic if for any four vertices u, v, w, x, the two larger of the thr... more A graph G = (V, E) is δ-hyperbolic if for any four vertices u, v, w, x, the two larger of the three distance sums d(u, v) + d(w, x), d(u, w) + d(v, x), d(u, x) + d(v, w) differ by at most 2δ ≥ 0. This paper describes the eccentricity terrain of a δ-hyperbolic graph. The eccentricity function e G (v) = max{d(v, u) : u ∈ V } partitions vertices of G into eccentricity layers C k (G) = {v ∈ V : e G (v) = rad(G) + k}, k ∈ N, where rad(G) = min{e G (v) : v ∈ V } is the radius of G. The paper studies the eccentricity layers of vertices along shortest paths, identifying such terrain features as hills, plains, valleys, terraces, and plateaus. It introduces the notion of β-pseudoconvexity, which implies Gromov's-quasiconvexity, and illustrates the abundance of pseudoconvex sets in δ-hyperbolic graphs. It shows that all sets C ≤k (G) = {v ∈ V : e G (v) ≤ rad(G) + k}, k ∈ N, are (2δ − 1)-pseudoconvex. Several bounds on the eccentricity of a vertex are obtained which yield a few approaches to efficiently approximating all eccentricities.
Discrete Mathematics, 2019
The δ-hyperbolicity of a graph is defined by a simple 4-point condition: for any four vertices u,... more The δ-hyperbolicity of a graph is defined by a simple 4-point condition: for any four vertices u, v, w, and x, the two larger of the distance sums d(u, v) + d(w, x), d(u, w) + d(v, x), and d(u, x) + d(v, w) differ by at most 2δ ≥ 0. Hyperbolicity can be viewed as a measure of how close a graph is to a tree metrically; the smaller the hyperbolicity of a graph, the closer it is metrically to a tree. A graph G is Helly if its disks satisfy the Helly property, i.e., every family of pairwise intersecting disks in G has a common intersection. It is known that for every graph G there exists the smallest Helly graph H(G) into which G isometrically embeds (H(G) is called the injective hull of G) and the hyperbolicity of H(G) is equal to the hyperbolicity of G. Motivated by this, we investigate structural properties of Helly graphs that govern their hyperbolicity and identify three isometric subgraphs of the King-grid as structural obstructions to a small hyperbolicity in Helly graphs.
2016 IEEE International Conference on Software Maintenance and Evolution (ICSME)
An approach to automatically recover the name of the branch where a given commit is originally ma... more An approach to automatically recover the name of the branch where a given commit is originally made within a GitHub repository is presented and evaluated. This is a difficult task because in Git, the commit object does not store the name of the branch when it is created. Here this is termed the commit's branch of origin. Developers typically use branches in Git to group sets of changes that are related by task or concern. The approach recovers the branch of origin only within the scope of a single repository. The recovery process first uses Git's default merge commit messages and then examines the relationships between neighboring commits. The evaluation includes a simulation, an empirical examination of 40 repositories of opensource systems, and a manual verification. The evaluations show that the average accuracy exceeds 97% of all commits and the average precision exceeds 80%.
Discrete Mathematics, 2019
The δ-hyperbolicity of a graph is defined by a simple 4-point condition: for any four vertices u,... more The δ-hyperbolicity of a graph is defined by a simple 4-point condition: for any four vertices u, v, w, and x, the two larger of the distance sums d(u, v) + d(w, x), d(u, w) + d(v, x), and d(u, x) + d(v, w) differ by at most 2δ ≥ 0. Hyperbolicity can be viewed as a measure of how close a graph is to a tree metrically; the smaller the hyperbolicity of a graph, the closer it is metrically to a tree. A graph G is Helly if its disks satisfy the Helly property, i.e., every family of pairwise intersecting disks in G has a common intersection. It is known that for every graph G there exists the smallest Helly graph H(G) into which G isometrically embeds (H(G) is called the injective hull of G) and the hyperbolicity of H(G) is equal to the hyperbolicity of G. Motivated by this, we investigate structural properties of Helly graphs that govern their hyperbolicity and identify three isometric subgraphs of the King-grid as structural obstructions to a small hyperbolicity in Helly graphs.
Uploads
Papers by Heather Guarnera