Pablo San Segundo

A new DSATUR-based algorithm for exact vertex coloring

This paper describes a new exact algorithm PASS for the vertex coloring problem based on the well known DSATUR algorithm. At each step DSATUR maximizes saturation degree to select a new candidate vertex to color, breaking ties by maximum degree w.r.t. uncolored vertices. Later Sewell introduced a new tiebreaking strategy, which evaluated available colors for each vertex explicitly. PASS differs from Sewell in that it restricts its application to a particular set of vertices. Overall performance is improved when the new strategy is applied selectively instead of at every step. The paper also reports systematic experiments over 1500 random graphs and a subset of the DIMACS color benchmark.

Relaxed approximate coloring in exact maximum clique search

This paper presents selective coloring as a new paradigm for branch-and-bound exact maximum clique search. Approximate coloring has, in recent, years been at the heart of leading solvers in the field. Selective coloring proposes to relax coloring up to a certain threshold. The result is a less informed but lighter decision heuristic. Different operators for the remaining uncolored vertices give rise to algorithmic variants integrated in a new BBMCL framework. BBMCL allows for an interesting comparison between approximate coloring and degree-based decision heuristics. The paper also reports extensive empirical tests. Selective coloring algorithms are fastest for a large subset of the graphs considered.

Robust Global Feature Based Data Association With a Sparse Bit Optimized Maximum Clique Algorithm

This paper presents a robust solution to the mobile robotics data association problem based on solving the maximum clique problem (MCP) in a typically sparse correspondence graph, which contains compatibility information between pairs of observations and landmarks. Bit sparse optimizations are designed and implemented in a new algorithm BBMCS, which reduces computation and memory requirements of a leading general purpose maximum clique solver, to make it possibly the best exact sparse MCP algorithm currently found in the literature. BBMCS is reported to achieve very good results in terms of robustness with few assumptions on noise and visibility, while managing very reasonable computation time and memory usage even for complex large data association problems.

A new exact maximum clique algorithm for large and massive sparse graphs

This paper describes a new very efficient branch-and-bound exact maximum clique algorithm BBMCSP, designed for large and massive sparse graphs which appear frequently in real life problems from different fields.State-of-the-art exact maximum clique algorithms encode the adjacency matrix in full but when dealing with sparse graphs some form of compression is required. The new algorithm is based on a leading bit-parallel non-sparse solver but employs a novel sparse encoding for the adjacency matrix. Moreover, it also improves on recent optimizations proposed in literature for the sparse case such as core-based bounds.Reported results show that it is several orders of magnitude better than state-of-the-art. Moreover, a number of real networks with many millions of nodes are solved in a few seconds. New state-of-the-art exact maximum bit-parallel clique algorithm tailored for massive graphs.New sparse bit parallel encoding.Improved preprocessing to reduce the problem?s scale.

Exploiting CPU Bit Parallel Operations to Improve Efficiency in Search

Cerebral aneurysms are weak or thin spots on blood vessels in the brain that balloon out. While the majority of aneurysms do not burst, those that do would lead to serious complications including hemorrhagic stroke, permanent nerve damage, or death. Yet, surgical options for treating cerebral aneurysms carry high risk to the patient. It is vital for the doctors to accurately diagnose aneurysms that have high probabilities of rupturing. In this application, the patient dataset has many attributes, ranging from patient profile to results from diagnostic test and features extracted from brain images. Many of the attributes are discrete and have missing values. The dataset is also highly biased, with 15% unrupture cases and 85% rupture cases. Building a classifier that unerringly predicts the unrupture (rare) class is a challenge. In this paper, we describe a systematic approach to build such a classifier through suitable combination of data mining algorithms. Our approach automatically determines the optimal combination of these algorithms for a dataset. The system has an accuracy of 92% and is currently being deployed at the Huashan Hospital.

A novel clique formulation for the visual feature matching problem

This paper presents CCMM (acronym for image Clique Matching), a new deterministic algorithm for the visual feature matching problem when images have low distortion. CCMM is multi-hypothesis, i.e. for each feature to be matched in the original image it builds an association graph which captures pairwise compatibility with a subset of candidate features in the target image. It then solves optimum joint compatibility by searching for a maximum clique. CCMM is shown to be more robust than traditional RANSAC-based single-hypothesis approaches. Moreover, the order of the graph grows linearly with the number of hypothesis, which keeps computational requirements bounded for real life applications such as UAV image mosaicing or digital terrain model extraction. The paper also includes extensive empirical validation.

GPU-Mapping: Robotic Map Building with Graphical Multiprocessors

This article provides a broad perspective of the potential applicability of graphical processing units (GPUs) computing power in robotics, specifically in the well-known problem of two-dimensional (2-D) robotic mapping. There are three possible ways of exploiting these massively parallel devices: 1) parallelizing existing algorithms, 2) integrating already existing parallelized general purpose software, and 3) use of its high-computational capabilities in the inception of new algorithms. This article presents examples for all three options: parallelizing a popular implementation of the gridmapping algorithm, using a GPU open-source linear sparse system solver to address the problem of linear least squares graph minimization, and developing a novel method that can be efficiently parallelized and executed in a GPU for handling overlapping grid maps in a mapping with local maps algorithm. Large speedups are shown in the experiments, highlighting the importance of this technology in robotic software development in the near future, as is already the case in many other areas.

Improved initial vertex ordering for exact maximum clique search

This paper describes a new initial vertexordering procedure NEW_SORT designed to enhance approximate-colour exact algorithms for the maximum clique problem (MCP). NEW_SORT considers two different vertex orderings: degree and colour-based. The degree-based vertex ordering describes an improvement over a well-known vertex ordering used by exact solvers. Moreover, colour-based vertex orderings for the MCP have been traditionally considered suboptimal with respect to degree-based ones. NEW_SORT chooses the “best” of the two orderings according to a new evaluation function. The reported experiments on graphs taken from public datasets show that a leading exact solver using NEW_SORT —and further enhanced with a strong initial solution— can improve its performance very significantly (sometimes even exponentially).

Reusing the Same Coloring in the Child Nodes of the Search Tree for the Maximum Clique Problem

In this paper we present a new approach to reduce the computational time spent on coloring in one of the recent branch-and-bound algorithms for the maximum clique problem. In this algorithm candidates to the maximum clique are colored in every search tree node. We suggest that the coloring computed in the parent node is reused for the child nodes when it does not lead to many new branches. So we reuse the same coloring only in the nodes for which the upper bound is greater than the current best solution only by a small value \(\delta \). The obtained increase in performance reaches 70 % on benchmark instances.

An enhanced bitstring encoding for exact maximum clique search in sparse graphs

This paper describes BBMCW, a new efficient exact maximum clique algorithm tailored for large sparse graphs which can be bit-encoded directly into memory without a heavy performance penalty. These graphs occur in real-life problems when some form of locality may be exploited to reduce their scale. One such example is correspondence graphs derived from data association problems. The new algorithm is based on the bit-parallel kernel used by the BBMC family of published exact algorithms. BBMCW employs a new bitstring encoding that we denote ‘watched’, because it is reminiscent of the ‘watched literal’ technique used in satisfiability and other constraint problems. The new encoding reduces the number of spurious operations computed by the BBMC bit-parallel kernel in large sparse graphs. Moreover, BBMCW also improves on bound computation proposed in the literature for bit-parallel solvers. Experimental results show that the new algorithm performs better than prior algorithms over data sets of both real and synthetic sparse graphs. In the real data sets, the improvement in performance averages more than two orders of magnitude with respect to the state-of-the-art exact solver IncMaxCLQ.