arXiv subjects

Pablo San Segundo

Publications and source records attributed to Pablo San Segundo.

4 recordsLinked to original sources

arXiv2026

An Integer Programming Approach to Compute Lower Bounds for Ramsey Numbers Using Circulant Graphs

The Ramsey number $R(m,n)$ is the smallest order at which every red-blue edge coloring of a complete graph must contain a blue clique (a complete subgraph) of size $m$ or a red clique of size $n$. Determining these numbers exactly is extremely hard, and even certifying a lower bound requires exhibiting an explicit coloring that avoids both cliques. We develop an integer programming framework for certifying such lower bounds, restricting the search to circulant graphs, whose rotational symmetry lets us reformulate the problem in a projected distance space, reducing the number of binary variables from quadratic to linear in the graph order. We strengthen this projected model through coefficient reduction and solve it with a branch-and-cut algorithm whose separation routine exploits the common neighborhood structure of circulant graphs, combining heuristic and exact maximum-clique algorithms. In an extensive computational campaign on circulant graphs with up to 410 vertices, we improve the best lower bounds previously obtained by other methods by up to 11 points for 25 values of $R(3,n)$ with $24\le n\le49$ and $n\neq27$, each backed by an explicit graph certificate that can be independently verified with a stand-alone exact clique solver. To the best of our knowledge, our method also provides the first reproducible optimization-based procedure for certifying circulant Ramsey numbers $R_C(m,n)$, which we use to establish eight new values of $R_C(3,n)$ with $13\le n\le20$. Our framework, graph certificates, and stand-alone checker are provided as supplementary material to support independent verification and reuse.

math.OC↗

arXiv2026

Loop Closure via Maximal Cliques in 3D LiDAR-Based SLAM

Reliable loop closure detection remains a critical challenge in 3D LiDAR-based SLAM, especially under sensor noise, environmental ambiguity, and viewpoint variation conditions. RANSAC is often used in the context of loop closures for geometric model fitting in the presence of outliers. However, this approach may fail, leading to map inconsistency. We introduce a novel deterministic algorithm, CliReg, for loop closure validation that replaces RANSAC verification with a maximal clique search over a compatibility graph of feature correspondences. This formulation avoids random sampling and increases robustness in the presence of noise and outliers. We integrated our approach into a real- time pipeline employing binary 3D descriptors and a Hamming distance embedding binary search tree-based matching. We evaluated it on multiple real-world datasets featuring diverse LiDAR sensors. The results demonstrate that our proposed technique consistently achieves a lower pose error and more reliable loop closures than RANSAC, especially in sparse or ambiguous conditions. Additional experiments on 2D projection-based maps confirm its generality across spatial domains, making our approach a robust and efficient alternative for loop closure detection.

cs.RO↗

arXiv2020

Research trends in combinatorial optimisation

Real-world problems are becoming highly complex and, therefore, have to be solved with combinatorial optimisation (CO) techniques. Motivated by the strong increase of publications on CO, 8,393 articles from this research field are subjected to a bibliometric analysis. The corpus of literature is examined using mathematical methods and a novel algorithm for keyword analysis. In addition to the most relevant countries, organisations and authors as well as their collaborations, the most relevant CO problems, solution methods and application areas are presented. Publications on CO focus mainly on the development or enhancement of metaheuristics like genetic algorithms. The increasingly problem-oriented studies deal particularly with real-world applications within the energy sector, production sector or data management, which are of increasing relevance due to various global developments. The demonstration of global research trends in CO can support researchers in identifying the relevant issues regarding this expanding and transforming research area.

econ.GN↗

arXiv2017

Efficiently Enumerating all Maximal Cliques with Bit-Parallelism

The maximal clique enumeration (MCE) problem has numerous applications in biology, chemistry, sociology, and graph modeling. Though this problem is well studied, most current research focuses on finding solutions in large sparse graphs or very dense graphs, while sacrificing efficiency on the most difficult medium-density benchmark instances that are representative of data sets often encountered in practice. We show that techniques that have been successfully applied to the maximum clique problem give significant speed gains over the state-of-the-art MCE algorithms on these instances. Specifically, we show that a simple greedy pivot selection based on a fixed maximum-degree first ordering of vertices, when combined with bit-parallelism, performs consistently better than the theoretical worst-case optimal pivoting of the state-of-the-art algorithms of Tomita et al. [Theoretical Computer Science, 2006] and Naudé [Theoretical Computer Science, 2016]. Experiments show that our algorithm is faster than the worst-case optimal algorithm of Tomita et al. on 60 out of 74 standard structured and random benchmark instances: we solve 48 instances 1.2 to 2.2 times faster, and solve the remaining 12 instances 3.6 to 47.6 times faster. We also see consistent speed improvements over the algorithm of Naudé: solving 61 instances 1.2 to 2.4 times faster. To the best of our knowledge, we are the first to achieve such speed-ups compared to these state-of-the-art algorithms on these standard benchmarks.

cs.DS↗