Papers by Pablo San Segundo
Computers & Operations Research, Jul 1, 2012
This paper describes a new exact algorithm PASS for the vértex coloring problem based on the well... more This paper describes a new exact algorithm PASS for the vértex coloring problem based on the well Keywords-known DSATUR algorithm. At each step DSATUR maximizes saturation degree to select a new candidate Color vértex to color, breaking ties by máximum degree w.r.t. uncolored vértices. Later Sewell introduced a Graph new tiebreaking strategy, which evaluated available colors for each vértex explicitly. PASS differs from Exact Sewell in that it restricts its application to a particular set of vértices. Overall performance is improved DSATUR 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.
CliSAT: A new exact algorithm for hard maximum clique problems
European Journal of Operational Research
Exploiting CPU Bit Parallel Operations to Improve Efficiency in Search
international conference on tools with artificial intelligence, Oct 29, 2007
It is the authors&amp... more It is the authors' belief that the ability of processors to compute bit parallel operations should have a right to exist as an optimization discipline, rather than a state-of- the-art technique. This paper is a step forward in this direction analysing a number of key issues related to bit model design and implementation of search problems. Building efficient search algorithms
International Transactions in Operational Research, 2021
Real-world problems are becoming highly complex and, therefore, have to be solved with combinator... more 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 problemoriented 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.
Real-world problems are becoming highly complex and, therefore, have to be solved with combinator... more 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 relevan...
Eur. J. Oper. Res., 2022
A binary constraint satisfaction problem (BCSP) consist in determining an assignment of values to... more A binary constraint satisfaction problem (BCSP) consist in determining an assignment of values to variables which is compatible with a set of constraints. The problem is called binary because the constraints involve only pairs of variables. The BCSP is a cornerstone problem in Constraint Programming (CP), appearing in a very wide range of real-world applications. In this work, we develop a new exact algorithm which effectively solves the BCSP by reformulating it as a k-clique problem on the underlying microstructure graph representation. Our new algorithm exploits the cutting-edge branching scheme of the state-ofthe-art maximum clique algorithms combined with two filtering phases in which the domains of the variables are reduced. Our filtering phases are based on coloring techniques and on heuristically solving an associated boolean satisfiability (SAT) problem. In addition, the algorithm initialization phase performs a reordering of the microstructure graph vertices which produces ...
Urban Transport XIV, 2008
In this work a direct method to measure the stability of metro system lines with respect to a pre... more In this work a direct method to measure the stability of metro system lines with respect to a previously constructed time schedule is presented. For this purpose we first model saturation effects using a real time discrete space state representation and then apply a Lyapunov-based stability analysis considering time delays of trains as disturbances. As a result we have been able to define a new set of indexes that relate time delays with the validity of the actual time schedule when falling inside a particular 'stability area'. Results obtained in a simulated environment show that the new stability indexes are able to evaluate quantitatively and qualitatively the effects of saturation in metro lines as well as predict the need for rescheduling
A new branch-and-bound algorithm for the Maximum Weighted Clique Problem
Computers & Operations Research
Abstract We study the Maximum Weighted Clique Problem (MWCP), a generalization of the Maximum Cli... more Abstract We study the Maximum Weighted Clique Problem (MWCP), a generalization of the Maximum Clique Problem in which weights are associated with the vertices of a graph. The MWCP calls for determining a complete subgraph of maximum weight. We design a new combinatorial branch-and-bound algorithm for the MWCP, which relies on an effective bounding procedure. The size of the implicit enumeration tree is largely reduced via a tailored branching scheme, specifically conceived for the MWCP. The new bounding function extends the classical MWCP bounds from the literature to achieve a good trade off between pruning potential and computing effort. We perform extensive tests on random graphs, graphs from the literature and real-world graphs, and we computationally show that our new exact algorithm is competitive with the state-of-the-art algorithms for the MWCP in all these classes of instances.
European Journal of Operational Research
Given a graph G and an interdiction budget k, the Maximum Clique Interdiction Problem asks to fin... more Given a graph G and an interdiction budget k, the Maximum Clique Interdiction Problem asks to find a subset of at most k vertices to remove from G so that the size of the maximum clique in the remaining graph is minimized. This problem has applications in many areas, such as crime detection, prevention of outbreaks of infectious diseases and surveillance of communication networks. We propose an integer linear programming formulation of the problem based on an exponential family of Clique-Interdiction Cuts and we give necessary and sufficient conditions under which these cuts are facet-defining. Our new approach provides a useful tool for analyzing the resilience of (social) networks with respect to clique-interdiction attacks, i.e., the decrease of the size of the maximum clique as a function of an incremental interdiction budget level. On a benchmark set of publicly available instances, including large-scale social networks with up to one hundred thousand vertices and three million edges, we show that most of them can be analyzed and solved to proven optimality within short computing time.
Computers & Operations Research
The maximal clique enumeration (MCE) problem has numerous applications in biology, chemistry, soc... more 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.
Improved Infra-Chromatic Bound for Exact Maximum Clique Search
Informatica
Planning as satisfiability is one of the most efficient ways to solve classic automated planning ... more Planning as satisfiability is one of the most efficient ways to solve classic automated planning problems. In SAT planning, the encoding used to convert the problem to a SAT formula is critical for the performance of the SAT solver. This paper presents a novel bit-encoding that reduces the number of bits required to represent actions in a SATbased automated planning problem. To obtain such encoding we first build a conflict graph, which represents incompatibilities of pairs of actions, and bitwise encode the subsets of actions determined by a clique partition. This reduces the number of Boolean variables and clauses of the SAT encoding, while preserving the possibility of parallel execution of compatible (non-neighbor) actions. The article also describes an appropriate algorithm for selecting the clique partition for this application and compares the new encodings obtained over some standard planning problems. CLASSICAL AUTOMATED PLANNING AS BOOLEAN SATISFIABILITY Automated Planning is a part of Artificial Intelligence that states the problem of selecting a course of actions to reach a goal. Classical automatic planning employs a planning model that on a domain description-typically an initial state and a goal state-and a set of actions that can change the current state. Classical domains have some restrictions: they are fully observable, deterministic, finite, static (that is, changes occur only when the planning agent acts), and discrete (in time, action, objects, and effects). Thus, the planning problem can be clearly defined and solved using a logical approach [1, 2]. Formally this is defined as a planning task = (, , ,) where:
An enhanced bitstring encoding for exact maximum clique search in sparse graphs
Optimization Methods and Software, 2017
This paper describes BBMCW, a new efficient exact maximum clique algorithm tailored for large spa... more 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.
An Enhanced Infra-Chromatic Bound for the Maximum Clique Problem
Lecture Notes in Computer Science, 2016
There has been a rising interest in experimental exact algorithms for the maximum clique problem ... more There has been a rising interest in experimental exact algorithms for the maximum clique problem because the gap between the expected theoretical performance and the reported results in practice is becoming surprisingly large. One reason for this is the family of bounding functions denoted as infra-chromatic because they produce bounds which can be lower than the chromatic number of the bounded subgraph. In this paper we describe a way to enhance exact solvers with an additional infra-chromatic bounding function and report performance over a number of graphs from well known data sets. Moreover, the reported results show that the new enhanced procedure significantly outperforms state-of-the-art.
Reusing the Same Coloring in the Child Nodes of the Search Tree for the Maximum Clique Problem
Lecture Notes in Computer Science, 2015
In this paper we present a new approach to reduce the computational time spent on coloring in one... more 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.
Studies in Computational Intelligence, 2013
This paper describes a new technique referred to as watched subgraphs which improves the performa... more This paper describes a new technique referred to as watched subgraphs which improves the performance of BBMC, a leading state of the art exact maximum clique solver (MCP). It is based on watched literals employed by modern SAT solvers for boolean constraint propagation. In efficient SAT algorithms, a list of clauses is kept for each literal (it is said that the clauses 'watch the literal) so that only those in the list are checked for constraint propagation when a (watched) literal is assigned during search. BBMC encodes vertex sets as bit strings, a bit block representing a subset of vertices (and the corresponding induced subgraph) the size of the CPU register word. The paper proposes to watch two subgraphs of critical sets during MCP search to efficiently compute a number of basic operations. Reported results validate the approach as the size and density of problem instances rise, while achieving comparable performance in the general case.
Infra-chromatic bound for exact maximum clique search
Computers & Operations Research, 2015
Many efficient exact branch and bound maximum clique solvers use approximate coloring to compute ... more Many efficient exact branch and bound maximum clique solvers use approximate coloring to compute an upper bound on the clique number for every subproblem. This technique reasonably promises tight bounds on average, but never tighter than the chromatic number of the graph.Li and Quan, 2010, AAAI Conference, p. 128-133 describe a way to compute even tighter bounds by reducing each colored subproblem to maximum satisfiability problem (MaxSAT). Moreover they show empirically that the new bounds obtained may be lower than the chromatic number.Based on this idea this paper shows an efficient way to compute related "infra-chromatic" upper bounds without an explicit MaxSAT encoding. The reported results show some of the best times for a stand-alone computer over a number of instances from standard benchmarks. New state-of-the-art exact maximum clique approximate color algorithm.Improved bounds possibly below the chromatic number.
A new combinatorial branch-and-bound algorithm for the Knapsack Problem with Conflicts
European Journal of Operational Research
A new branch-and-bound algorithm for the maximum edge-weighted clique problem
European Journal of Operational Research
Applied Intelligence, 2016
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Papers by Pablo San Segundo