arXiv subjects

Jesper Jansson

Publications and source records attributed to Jesper Jansson.

9 recordsLinked to original sources

arXiv2026

Burning Graph Powers and Branching Trees

Graph burning is a discrete-time process that models the spread of social contagion. Initially, all vertices are unburned. In each round, one unburned vertex is selected and burned, while any unburned vertex that has a burned neighbour from the previous round also becomes burned. The burning number of a graph is the minimum number of rounds needed to burn the entire graph. In this paper, we study the burning number of graph powers. First, we show that for a connected graph~$G$, its graph power~$G^k$ contains a~$(k+1)^+$-branching tree as a spanning tree. A~$(k+1)^+$-branching tree is one in which all internal vertices have degree at least~$k+1$. We then show that $(k+1)^+$-branching trees on~$n$ vertices have burning number at most $\left\lceil{\sqrt{\frac{4(k-1)n}{k^2}}}~\right\rceil$. As the burning number of a graph is at most the burning number of any of its spanning trees, this gives an upper bound on the burning number of graph powers. We also derive an alternative upper bound on the burning number of~$k^+$-branching trees using the strongest currently known general burning number bound [Bastide et al.]. We then identify the ranges of~$k$ and~$n$ for which our bound outperforms or matches this alternative bound. Finally, we show that~$b(G^k) \le (1+o(1))\sqrt{n/k}$ based on the asymptotic burning number bound of Norin and Turcotte.

math.CO↗

arXiv2025

Graph-based method for constructing consensus trees

A consensus tree is a phylogenetic tree that synthesizes a given collection of phylogenetic trees, all of which share the same leaf labels but may have different topologies, typically obtained through bootstrapping. Our research focuses on creating a consensus tree from a collection of phylogenetic trees, each detailed with branch-length data. We integrate branch lengths into the consensus to encapsulate the progression rate of genetic mutations. However, traditional consensus trees, such as the strict consensus tree, primarily focus on the topological structure of these trees, often neglecting the informative value of branch lengths. This oversight disregards a crucial aspect of evolutionary study and highlights a notable gap in traditional phylogenetic approaches. In this paper, we extend \textit{PrimConsTree}\footnote{A preliminary version of this article was presented at \emph{the Fifteenth International Conference on Bioscience, Biochemistry, and Bioinformatics (ICBBB~2025)}~(reference~\cite{torquet2005icbbb}).}, a graph-based method for constructing consensus trees. This algorithm incorporates topological information, edge frequency, clade frequency, and branch length to construct a more robust and comprehensive consensus tree. Our adaptation of the well-known Prim algorithm efficiently identifies the maximum frequency branch and maximum frequency nodes to build the optimal consensus tree. This strategy was pre-processed with clustering steps to calibrate the robustness and accuracy of the consensus tree.\\ \textbf{Availability and implementation:} The source code of PrimConsTree is freely available on GitHub at https://github.com/tahiri-lab/PrimConsTree.

q-bio.PE↗

arXiv2025

Multiplication of 0-1 matrices via clustering

We study applications of clustering (in particular, the $k$-center clustering problem) in the design of efficient and practical algorithms for computing an approximate and the exact arithmetic matrix product of two 0-1 rectangular matrices with clustered rows or columns, respectively. Our results in part can be regarded as an extension of the clustering-based approach to Boolean square matrix multiplication due to Arslan and Chidri (CSC 2011). First, we provide a simple and efficient deterministic algorithm for approximate matrix product of 0-1 matrices, where the additive error is proportional to the minimum maximum radius in an $\ell$-center clustering of the rows of the first matrix or an $k$-center clustering of the columns of the second matrix. Next, we use the approximation algorithm as a preprocessing after which a query asking for the exact value of an arbitrary entry in the product matrix can be answered in time proportional to the additive error. As a consequence, we obtain a simple deterministic algorithm for the exact matrix product of 0-1 matrices. We also present an improved simple deterministic algorithm for the exact product and in addition, faster analogous randomized algorithms for an approximate and the exact matrix products of 0-1 matrices based on randomized $\ell$ and $k$-center clustering.

cs.DS↗

arXiv2024

The Voronoi Diagram of Weakly Smooth Planar Point Sets in $O(\log n)$ Deterministic Rounds on the Congested Clique

We study the problem of computing the Voronoi diagram of a set of $n^2$ points with $O(\log n)$-bit coordinates in the Euclidean plane in a substantially sublinear in $n$ number of rounds in the congested clique model with $n$ nodes. Recently, Jansson et al. have shown that if the points are uniformly at random distributed in a unit square then their Voronoi diagram within the square can be computed in $O(1)$ rounds with high probability (w.h.p.). We show that if a very weak smoothness condition is satisfied by an input set of $n^2$ points with $O(\log n)$-bit coordinates in the unit square then the Voronoi diagram of the point set within the unit square can be computed in $O(\log n)$ rounds in this model.

cs.CG↗

arXiv2023

Convex Hulls, Triangulations, and Voronoi Diagrams of Planar Point Sets on the Congested Clique

We consider geometric problems on planar $n^2$-point sets in the congested clique model. Initially, each node in the $n$-clique network holds a batch of $n$ distinct points in the Euclidean plane given by $O(\log n)$-bit coordinates. In each round, each node can send a distinct $O(\log n)$-bit message to each other node in the clique and perform unlimited local computations. We show that the convex hull of the input $n^2$-point set can be constructed in $O(\min\{ h,\log n\})$ rounds, where $h$ is the size of the hull, on the congested clique. We also show that a triangulation of the input $n^2$-point set can be constructed in $O(\log^2n)$ rounds on the congested clique. Finally, we demonstrate that the Voronoi diagram of $n^2$ points with $O(\log n)$-bit coordinates drawn uniformly at random from a unit square can be computed within the square with high probability in $O(1)$ rounds on the congested clique.

cs.DC↗

arXiv2021

Efficient Assignment of Identities in Anonymous Populations

We consider the fundamental problem of assigning distinct labels to agents in the probabilistic model of population protocols. Our protocols operate under the assumption that the size $n$ of the population is embedded in the transition function. Our labeling protocols are silent w.h.p., i.e., eventually each agent reaches its final state and remains in it forever w.h.p., as well as safe, i.e., never update the label assigned to any single agent. We first present a fast, silent w.h.p.and safe labeling protocol for which the required number of interactions is asymptotically optimal, i.e., $O(n \log n/ε)$ w.h.p. It uses $(2+ε)n+O(n^c)$ states, for any $c<1,$ and the label range $1,\dots,(1+ε)n.$ Furthermore, we consider the so-called pool labeling protocols that include our fast protocol. We show that the expected number of interactions required by any pool protocol is $\ge \frac{n^2}{r+1}$, when the labels range is $1,\dots, n+r<2n.$ Next, we provide a protocol which is silent and safe once a unique leader is provided, and uses only $n+5\sqrt n +O(n^c)$ states, for any $c<1,$ and draws labels from the range $1,\dots,n.$ The expected number of interactions required by the protocol is $O(n^3).$ On the other hand, we show that (even if a unique leader is given in advance) any silent protocol that produces a valid labeling and is safe with probability $>1-\frac 1n$, uses $\ge n+\sqrt {n-1} -1$ states. Hence, our protocol is almost state-optimal. We also present a generalization of the protocol to include a trade-off between the number of states and the expected number of interactions. Furthermore, we show that for any silent and safe labeling protocol utilizing $n+t<2n$ states the expected number of interactions required to achieve a valid labeling is $\ge \frac{n^2}{t+1}$.

cs.DC↗

arXiv2021

New and Improved Algorithms for Unordered Tree Inclusion

The tree inclusion problem is, given two node-labeled trees $P$ and $T$ (the ``pattern tree'' and the ``target tree''), to locate every minimal subtree in $T$ (if any) that can be obtained by applying a sequence of node insertion operations to $P$. Although the ordered tree inclusion problem is solvable in polynomial time, the unordered tree inclusion problem is NP-hard. The currently fastest algorithm for the latter is a classic algorithm by Kilpeläinen and Mannila from 1995 that runs in $O(2^{2d} mn)$ time, where $m$ and $n$ are the sizes of the pattern and target trees, respectively, and $d$ is the degree of the pattern tree. Here, we develop a new algorithm that runs in $O(2^{d} mn^2)$ time, improving the exponential factor from $2^{2d}$ to $2^d$ by considering a particular type of ancestor-descendant relationships that is suitable for dynamic programming. We also study restricted variants of the unordered tree inclusion problem.

cs.DS↗

arXiv2013

Algorithms for the Majority Rule (+) Consensus Tree and the Frequency Difference Consensus Tree

This paper presents two new deterministic algorithms for constructing consensus trees. Given an input of k phylogenetic trees with identical leaf label sets and n leaves each, the first algorithm constructs the majority rule (+) consensus tree in O(kn) time, which is optimal since the input size is Omega(kn), and the second one constructs the frequency difference consensus tree in min(O(kn^2), O(kn (k+log^2 n))) time.

cs.DS↗

arXiv2012

CRAM: Compressed Random Access Memory

We present a new data structure called the \emph{Compressed Random Access Memory} (CRAM) that can store a dynamic string $T$ of characters, e.g., representing the memory of a computer, in compressed form while achieving asymptotically almost-optimal bounds (in terms of empirical entropy) on the compression ratio. It allows short substrings of $T$ to be decompressed and retrieved efficiently and, significantly, characters at arbitrary positions of $T$ to be modified quickly during execution \emph{without decompressing the entire string}. This can be regarded as a new type of data compression that can update a compressed file directly. Moreover, at the cost of slightly increasing the time spent per operation, the CRAM can be extended to also support insertions and deletions. Our key observation that the empirical entropy of a string does not change much after a small change to the string, as well as our simple yet efficient method for maintaining an array of variable-length blocks under length modifications, may be useful for many other applications as well.

cs.DS↗