arXiv subjects

Jeroen S. K. Lamme

Publications and source records attributed to Jeroen S. K. Lamme.

3 recordsLinked to original sources

arXiv2026

Touring a Sequence of Orthogonal Polygons

We study the problem of computing a shortest tour that visits a sequence of $k$ polygons $P_1,\dots, P_k$ with a total number of $n$ vertices. A tour is an oriented curve such that there exist points $p_i\in P_i$ for all $i$ where $p_i$ appears not after $p_{i+1}$. In a seminal paper, Dror, Efrat, Lubiw and Mitchell (STOC 2003) considered the problem under $L_2$ distance, and gave $\widetilde O(nk)$ and $\widetilde O(nk^2)$ algorithms for disjoint and intersecting convex polygons, respectively. In this paper, we consider the orthogonal setting (with orthogonal polygons and Manhattan distance) and obtain the following results: - a truly subquadratic $\widetilde O(n^{2-\frac{1}{48}})$ algorithm when consecutive polygons in the sequence are disjoint; - an $\widetilde O(n)$ algorithm for ortho-convex polygons when consecutive polygons are disjoint; - an $O(n)$ algorithm for axis-aligned rectangles; - $\widetilde O(n^2)$ and $\widetilde O(n^{1.5}k^2)$ algorithms without restrictions. Our algorithms build on a wide range of techniques, including additively weighted Voronoi diagrams, rectangle decompositions, persistent data structures, and dynamic distance oracles for weighted planar graphs.

cs.CG↗

arXiv2026

Single-Source Shortest Paths and Almost Exact Diameter in Pseudodisk Graphs

We study SINGLE-SOURCE SHORTEST PATH (SSSP) on unweighted intersection graphs whose node set corresponds to a set of $n$ constant-complexity objects in the plane. We prove SSSP can be solved in $O(U(n)\ \mathrm{polylog}\,n)$ expected time for any class of objects whose union complexity is $U(n)$. In particular, we obtain an $O(n 2^{α(n)}\log^2 n)$ algorithm for arbitrary pseudodisks, and an $O(λ_{s+2}(n)2^{O(\log^* n)} \log^2 n)$ algorithm for locally fat objects. This significantly extends the class of objects for which SSSP can be solved in $O(n\ \mathrm{polylog}\, n)$ time: so far, $O(n\ \mathrm{polylog}\, n)$ SSSP algorithms were not even known for pseudodisks that are fat and convex and similarly-sized. Our second result concerns the DIAMETER problem, which asks for the maximum distance between any two nodes in a graph. Even for intersection graphs, near-quadratic algorithms are difficult to obtain, and the $O(n^2\ \mathrm{polylog}\, n)$ running time that follows from our SSSP algorithm is the first near-quadratic running time for such general classes of intersection graphs. Obtaining subquadratic running time is even more challenging. We prove that the diameter of a set of arbitrary pseudodisks can be computed almost exactly, namely up to an additive error of 2, in $\tilde{O}(n^{2-1/14})$ expected time. This generalizes and speeds up a recent algorithm by Chang, Gao, and Le~(SoCG 2024) that works for similarly-sized disks (or similarly-sized pseudodisks that are fat and satisfy a strong monotonicity assumption) and runs in $\tilde{O}(n^{2-1/18})$ time. To this end, we develop a so-called star-based $r$-clustering for intersection graphs of pseudodisks, which is interesting in its own right. Our star-based $r$-clustering can also be used to obtain an almost exact distance oracle for pseudodisks that uses $O(n^{2-1/13})$ storage and has $O(1)$ query time.

cs.CG↗

arXiv2025

An ETH-Tight FPT Algorithm for Rejection-Proof Set Packing with Applications to Kidney Exchange

We study the parameterized complexity of a recently introduced multi-agent variant of the Kidney Exchange problem. Given a directed graph $G$ and integers $d$ and $k$, the standard problem asks whether $G$ contains a packing of vertex-disjoint cycles, each of length $\leq d$, covering at least $k$ vertices in total. In the multi-agent setting we consider, the vertex set is partitioned over several agents who reject a cycle packing as solution if it can be modified into an alternative packing that covers more of their own vertices. A cycle packing is called rejection-proof if no agent rejects it and the problem asks whether such a packing exists that covers at least $k$ vertices. We exploit the sunflower lemma on a set packing formulation of the problem to give a kernel for this $Σ_2^P$-complete problem that is polynomial in $k$ for all constant values of $d$. We also provide a $2^{\mathcal{O}(k \log k)} + n^{\mathcal{O}(1)}$ algorithm based on it and show that this FPT algorithm is asymptotically optimal under the ETH. Further, we generalize the problem by including an additional positive integer $c$ in the input that naturally captures how much agents can modify a given cycle packing to reject it. For every constant $c$, the resulting problem simplifies from being $Σ_2^P$-complete to NP-complete. The super-exponential lower bound already holds for $c=2$, though. We present an ad-hoc single-exponential algorithm for $c = 1$. These results reveal an interesting discrepancy between the classical and parameterized complexity of the problem and give a good view of what makes it hard.

cs.DS↗