arXiv subjects

Nicolás Honorato-Droguett

Publications and source records attributed to Nicolás Honorato-Droguett.

5 recordsLinked to original sources

arXiv2026

Algorithms for Optimally Shifting Intervals under Intersection Graph Models

We introduce Geometric Graph Edit Distance, a model for modifying geometric intersection graphs by moving objects. The objective is to obtain a graph in a prescribed class while minimising the total (weighted) moving distance of the objects. For weighted intervals of arbitrary length, we give a prune-and-search algorithm that renders their intersection graph complete in linear time. We adapt this approach to maximise the common intersection length of weighted intervals within a movement threshold in linear time. We also extend the algorithm for obtaining complete graphs to weighted axis-parallel rectangles of arbitrary size under the $L_1$ distance. For unweighted unit intervals, we give an $O(n\log n)$-time algorithm for obtaining a graph containing a $k$-clique. Lastly, we give $O(n)$-size linear programs for obtaining graphs in several classes, including edgeless, acyclic, $k$-clique-free and $k$-connected graphs.

cs.DS↗

arXiv2026

Moving Geometric Objects to Render Their Intersection Graph Connected or Locally Dense

In this paper, we study graph editing problems on geometric intersection graphs. For a tuple $\mathcal{S}=(S_1,\dots,S_n)$ of geometric objects in some Euclidean space, let $G_\mathcal{S}$ be their intersection graph. We study the problem of finding a tuple $D=(d_1,\dots,d_n)$ of movement vectors such that the resulting intersection graph $G_{\mathcal{S}+D}$ (after moving, for every $i \in \{1,\dots,n\}$, object $S_i$ by $d_i$) has a predefined property and the total movement distance $|D|$ is minimum. In the weighted version, we are also given a weight vector $w=(w_1,\dots,w_n)$ with positive entries, and the objective is to minimise the total weighted movement distance $|w \cdot D|$. We first consider the property locally dense, which we define as containment of a $k$-clique. Given $n$ weighted intervals, we solve the problem with respect to this property in $O(k^{1/3} n \log^{1+\varepsilon} n)$ time for any $\varepsilon>0$. We then consider $k$-connectivity for $1\le k \le n-1$. Given $n$ unweighted unit intervals, we solve the problem in $O(n^2 \log n)$ time and, for $k=1$, in $O(n\log n)$ time. For $k=1$, we prove strong NP-hardness on intervals of arbitrary length and on weighted unit disks (with only two distinct weights), and weak NP-hardness on weighted intervals (even when lengths equal weights).

cs.CG↗

arXiv2026

Linear-Time Transformations Between Connectivity Maintenance and Points Spreading on Linear and Cyclic Domains

Given $n$ points on a line or closed cycle and a threshold $r>0$, the connectivity-maintenance problem is to move the points so that every gap between consecutive points is at most $r$, whereas the points-spreading problem requires every gap to be at least $r$. Li and Wang [CCCG 2015; CGT 2025] and Chen, Gu, Li, and Wang [SWAT 2012; DCG 2013] gave $O(n)$-time algorithms for the cyclic versions of min-max points-spreading and min-max connectivity-maintenance, respectively. Ghadiri and Yazdanbod [CCCG 2016] gave an $O(n\log n)$-time algorithm for the linear version of min-sum points-spreading. In this paper, we show that the two problems can be reduced in linear time to each other for both objectives and on both linear and cyclic domains. As an implication, min-sum connectivity-maintenance is solvable in $O(n\log n)$ time on both domains. Finally, we extend the reduction to points on a line with individual thresholds when their initial order is preserved.

cs.CG↗

arXiv2026

Further Results on Rendering Geometric Intersection Graphs Sparse by Dispersion

Removing overlaps is a central task in domains such as scheduling, visibility, and map labelling. This can be modelled using graphs, where overlap removals correspond to enforcing a certain sparsity constraint on the graph structure. We continue the study of the problem Geometric Graph Edit Distance (GGED), where the aim is to minimise the total cost of editing a geometric intersection graph to obtain a graph contained in a specific graph class. For us, the edit operation is the movement of objects, and the cost is the movement distance. We present an algorithm for rendering the intersection graph of a set of unit circular arcs edgeless and $k$-clique-free in $O(n\log n)$ time, where $n$ is the number of arcs. The algorithm can be also used to solve an open case of the points-spreading problem on cyclic domains [Li \& Wang, CGT 2025]. We also show that GGED remains strongly NP-hard on unweighted interval graphs, solving an open problem of Honorato-Droguett et al. [WADS 2025]. We complement this result by showing that GGED is strongly NP-hard on sets of $d$-balls and $d$-cubes, for any $d\ge 2$. Finally, we present an XP algorithm (parameterised by the number of maximal cliques) that removes all edges from the intersection graph of a set of weighted unit intervals.

cs.CG↗

arXiv2025

On the Complexity of Minimising the Moving Distance for Dispersing Objects

We study Geometric Graph Edit Distance (GGED), a graph-editing model to compute the minimum edit distance of intersection graphs that uses moving objects as an edit operation. We first show an $O(n\log n)$-time algorithm that minimises the total moving distance to disperse unit intervals. This algorithm is applied to render a given unit interval graph (i) edgeless, (ii) acyclic and (iii) $k$-clique-free. We next show that GGED becomes strongly NP-hard when rendering a weighted interval graph (i) edgeless, (ii) acyclic and (iii) $k$-clique-free. Lastly, we prove that minimising the maximum moving distance for rendering a unit disk graph edgeless is strongly NP-hard over the $L_1$ and $L_2$ distances.

cs.DS↗