The Strassen $2\times2$ matrix multiplication algorithm arises from the volume form on the 3-dimensional quotient space of the $2\times 2$ matrices by the multiples of identity.
We reduce the additive cost of general (non-commutative) 3x3 matrix multiplication from the previous records of 61 (Schwartz-Vaknin, 2023) and 62 (Martensson-Wagner, 2025) to 60 without a change of basis. To our knowledge, this represents a new state-of-the-art.
In the 3-Hitting Set problem, the input is a hypergraph $G$ such that the size of every hyperedge of $G$ is at most 3, and an integers $k$, and the goal is to decide whether there is a set $S$ of at most $k$ vertices such that every hyperedge of $G$ contains at least one vertex from $S$. In this paper we give an $O^*(2.0409^k)$-time algorithm for 3-Hitting Set.
This paper investigates the non-clairvoyant parallel machine scheduling problem with prediction, with the objective of minimizing the makespan. Improved lower bounds for the problem and competitive ratios of online algorithms with respect to the prediction error are presented for both the non-preemptive and preemptive cases on m identical machines.
We give the first algorithm for adaptive alphabetic prefix-free coding that is worst-case optimal in terms of time and compression when $σ\in o \left( \frac{n^{1 / 2}}{\log n} \right)$, where $σ$ is the size of the alphabet and $n$ is the length of the input.
This article briefly describes four algorithmic problems where the notion of treewidth is very useful. Even though the problems themselves have nothing to do with treewidth, it turns out that combining known results on treewidth allows us to easily describe very clean and high-level algorithms.
We slightly improve the known lower bound on the asymptotic competitive ratio for online bin packing of rectangles. We present a complete proof for the new lower bound, whose value is above 1.91.
This paper explains a subtle issue in the martingale analysis of the IMM algorithm, a state-of-the-art influence maximization algorithm. Two workarounds are proposed to fix the issue, both requiring minor changes on the algorithm and incurring a slight penalty on the running time of the algorithm.
We present the first thorough practical study of the Lempel-Ziv-78 and the Lempel-Ziv-Welch computation based on trie data structures. With a careful selection of trie representations we can beat well-tuned popular trie data structures like Judy, m-Bonsai or Cedar.
We present an adaptive tester for the unateness property of Boolean functions. Given a function $f:\{0,1\}^n \to \{0,1\}$ the tester makes $O(n \log(n)/ε)$ adaptive queries to the function. The tester always accepts a unate function, and rejects with probability at least 0.9 if a function is $ε$-far from being unate.
We provide a decremental approximate Distance Oracle that obtains stretch of $1+ε$ multiplicative and 2 additive and has $\hat{O}(n^{5/2})$ total cost (where $\hat{O}$ notation suppresses polylogarithmic and $n^{O(1)/\sqrt{n}}$ factors). The best previous results with $\hat{O}(n^{5/2})$ total cost obtained stretch $3+ε$.
A Dynamic Programming based polynomial worst case time and space algorithm is described for computing Hamiltonian Path of a directed graph. Complexity constructive proofs along with a tested C++ implementation are provided as well. The result is obtained via the use of original colored hypergraph structures in order to maintain and update the necessary DP states.
In this paper, we propose a new ranking method inspired from previous results on the diffusion approach to solve linear equation. We describe new mathematical equations corresponding to this method and show through experimental results the potential computational gain. This ranking method is also compared to the well known PageRank model.
Pascal Berthomé, Jean-François Lalande, Vincent Levorato
This technical report describes the implementation of exact and parametrized exponential algorithms, developed during the French ANR Agape during 2010-2012. The developed algorithms are distributed under the CeCILL license and have been written in Java using the Jung graph library.
We present a practical algorithm for the cyclic longest common subsequence (CLCS) problem that runs in O(mn) time, where m and n are the lengths of the two input strings. While this is not necessarily an asymptotic improvement over the existing record, it is far simpler to understand and to implement.
This paper introduces a new data structure, log_vector, with the following properties: constant time random access to individual elements; constant time element addition to the end; constant time element removal from the end; constant time empty data structure creation; amortized constant space per individual elements; constant additional space used.
Antoine Thomas, Aïda Ouangraoua, Jean-Stéphane Varré
We address the problem of finding the minimal number of block interchanges (exchange of two intervals) required to transform a duplicated linear genome into a tandem duplicated linear genome. We provide a formula for the distance as well as a polynomial time algorithm for the sorting problem.