ALBCOM  Algorismia, Bioinformàtica, Complexitat i Mètodes Formals
http://hdl.handle.net/2117/3092
20160827T06:35:12Z

Absorption time of the Moran process
http://hdl.handle.net/2117/89367
Absorption time of the Moran process
Díaz Cort, Josep; Goldberg, Leslie Ann; Richerby, David; Serna Iglesias, María José
© 2016 Wiley Periodicals, Inc.
The Moran process models the spread of mutations in populations on graphs. We investigate the absorption time of the process, which is the time taken for a mutation introduced at a randomly chosen vertex to either spread to the whole population, or to become extinct. It is known that the expected absorption time for an advantageous mutation is O(n4) on an nvertex undirected graph, which allows the behaviour of the process on undirected graphs to be analysed using the Markov chain Monte Carlo method. We show that this does not extend to directed graphs by exhibiting an infinite family of directed graphs for which the expected absorption time is exponential in the number of vertices. However, for regular directed graphs, we show that the expected absorption time is O(nlogn) and O(n2). We exhibit families of graphs matching these bounds and give improved bounds for other families of graphs, based on isoperimetric number. Our results are obtained via stochastic dominations which we demonstrate by establishing a coupling in a related continuoustime model. The coupling also implies several natural domination results regarding the fixation probability of the original (discretetime) process, resolving a conjecture of Shakarian, Roos and Johnson.
20160729T13:05:23Z
Díaz Cort, Josep
Goldberg, Leslie Ann
Richerby, David
Serna Iglesias, María José
© 2016 Wiley Periodicals, Inc.
The Moran process models the spread of mutations in populations on graphs. We investigate the absorption time of the process, which is the time taken for a mutation introduced at a randomly chosen vertex to either spread to the whole population, or to become extinct. It is known that the expected absorption time for an advantageous mutation is O(n4) on an nvertex undirected graph, which allows the behaviour of the process on undirected graphs to be analysed using the Markov chain Monte Carlo method. We show that this does not extend to directed graphs by exhibiting an infinite family of directed graphs for which the expected absorption time is exponential in the number of vertices. However, for regular directed graphs, we show that the expected absorption time is O(nlogn) and O(n2). We exhibit families of graphs matching these bounds and give improved bounds for other families of graphs, based on isoperimetric number. Our results are obtained via stochastic dominations which we demonstrate by establishing a coupling in a related continuoustime model. The coupling also implies several natural domination results regarding the fixation probability of the original (discretetime) process, resolving a conjecture of Shakarian, Roos and Johnson.

Process mining meets abstract interpretation
http://hdl.handle.net/2117/88077
Process mining meets abstract interpretation
Carmona Vargas, Josep; Cortadella Fortuny, Jordi
The discovery of process models out of system traces is an interesting problem that has received significant attention in the last years. In this work, a theory for the derivation of a Petri net from a set of traces is presented. The method is based on the theory of abstract interpretation, which has been applied successfully in other areas. The principal application of the theory presented is Process Mining, an area that tries to incorporate the use of formal models both in the design and use of information systems.
20160616T08:50:11Z
Carmona Vargas, Josep
Cortadella Fortuny, Jordi
The discovery of process models out of system traces is an interesting problem that has received significant attention in the last years. In this work, a theory for the derivation of a Petri net from a set of traces is presented. The method is based on the theory of abstract interpretation, which has been applied successfully in other areas. The principal application of the theory presented is Process Mining, an area that tries to incorporate the use of formal models both in the design and use of information systems.

Process mining from a basis of state regions
http://hdl.handle.net/2117/88012
Process mining from a basis of state regions
Solé, Marc; Carmona Vargas, Josep
A central problem in the area of Process Mining is to obtain a formal model that represents selected behavior of a system. The theory of regions has been applied to address this problem, enabling the derivation of a Petri net whose language includes a set of traces. However, when dealing with reallife systems, the available tool support for performing such task is unsatisfactory, due to the complex algorithms that are required. In this paper, the theory of regions is revisited to devise a novel technique that explores the space of regions by combining the elements of a region basis. Due to its light space requirements, the approach can represent an important step for bridging the gap between the theory of regions and its industrial application. Experimental results improve in orders of magnitude stateoftheart tools for the same task.
20160615T07:59:02Z
Solé, Marc
Carmona Vargas, Josep
A central problem in the area of Process Mining is to obtain a formal model that represents selected behavior of a system. The theory of regions has been applied to address this problem, enabling the derivation of a Petri net whose language includes a set of traces. However, when dealing with reallife systems, the available tool support for performing such task is unsatisfactory, due to the complex algorithms that are required. In this paper, the theory of regions is revisited to devise a novel technique that explores the space of regions by combining the elements of a region basis. Due to its light space requirements, the approach can represent an important step for bridging the gap between the theory of regions and its industrial application. Experimental results improve in orders of magnitude stateoftheart tools for the same task.

Multikey Quickselect
http://hdl.handle.net/2117/88009
Multikey Quickselect
Frias Moya, Leonor; Roura Ferret, Salvador
In this paper we introduce Multikey Quickselect: an efficient, inplace, and easy to implement algorithm for the selection problem for strings. We present several variants of our basic algorithm, which apply to two different flavors of the selection problem. Also, we analyze the cost of the main variants, measured as the expected number of character comparisons and elements swaps. Some of the enhancements presented in this paper apply to Multikey Quicksort as well.
20160615T07:21:39Z
Frias Moya, Leonor
Roura Ferret, Salvador
In this paper we introduce Multikey Quickselect: an efficient, inplace, and easy to implement algorithm for the selection problem for strings. We present several variants of our basic algorithm, which apply to two different flavors of the selection problem. Also, we analyze the cost of the main variants, measured as the expected number of character comparisons and elements swaps. Some of the enhancements presented in this paper apply to Multikey Quicksort as well.

The HOM problem is decidable
http://hdl.handle.net/2117/87972
The HOM problem is decidable
Godoy, Guillem; Giménez, Omer; Ramos Garrido, Lander; Álvarez Faura, M. del Carme
We close affirmatively a question which has been open for 35 years: decidability of the HOM problem. The HOM problem consists in deciding, given a tree homomorphism $H$ and a regular tree languagle $L$ represented by a tree automaton, whether $H(L)$ is regular. For deciding the HOM problem, we develop new constructions and techniques which are interesting by themselves, and provide several significant intermediate results. For example, we prove that the universality problem is decidable for languages represented by tree automata with equality constraints, and that the equivalence and inclusion problems are decidable for images of regular languages through tree homomorphisms. Our contributions are based on the following new results. We describe a simple transformation for converting a tree automaton with equality constraints into a tree automaton with disequality constraints recognizing the complementary language. We also define a new class of automaton with arbitrary disequality constraints and a particular kind of equality constraints. This new class essentially recognizes the intersection of a tree automaton with disequality constraints and the image of a regular language through a tree homomorphism. We prove decidability of emptiness and finiteness for this class by a pumping mechanism. The above constructions are combined adequately to provide an algorithm deciding the HOM problem.
20160614T11:51:17Z
Godoy, Guillem
Giménez, Omer
Ramos Garrido, Lander
Álvarez Faura, M. del Carme
We close affirmatively a question which has been open for 35 years: decidability of the HOM problem. The HOM problem consists in deciding, given a tree homomorphism $H$ and a regular tree languagle $L$ represented by a tree automaton, whether $H(L)$ is regular. For deciding the HOM problem, we develop new constructions and techniques which are interesting by themselves, and provide several significant intermediate results. For example, we prove that the universality problem is decidable for languages represented by tree automata with equality constraints, and that the equivalence and inclusion problems are decidable for images of regular languages through tree homomorphisms. Our contributions are based on the following new results. We describe a simple transformation for converting a tree automaton with equality constraints into a tree automaton with disequality constraints recognizing the complementary language. We also define a new class of automaton with arbitrary disequality constraints and a particular kind of equality constraints. This new class essentially recognizes the intersection of a tree automaton with disequality constraints and the image of a regular language through a tree homomorphism. We prove decidability of emptiness and finiteness for this class by a pumping mechanism. The above constructions are combined adequately to provide an algorithm deciding the HOM problem.

Speculation in elastic systems
http://hdl.handle.net/2117/87919
Speculation in elastic systems
Galcerán Oms, Marc; Cortadella Fortuny, Jordi; Kishinevsky, Mike
Speculation is a wellknown technique for increasing parallelism of the microprocessor pipelines and hence their performance. While implementing speculation in modern design practice is errorprone
and mostly adhoc, this paper proposes a correctbyconstruction method for implementing speculation in Elastic Systems. The technique is based on applying provably correct transformations such as early
evaluation, insertion of antitokens and bubbles, retiming, and sharing. It allows to explore different microarchitectural solutions for better design tradeoffs. The benefits of speculation are illustrated with
two examples in which these transformations are systematically applied. The method proposed in this paper is amenable for automation in a synthesis flow.
20160613T09:35:08Z
Galcerán Oms, Marc
Cortadella Fortuny, Jordi
Kishinevsky, Mike
Speculation is a wellknown technique for increasing parallelism of the microprocessor pipelines and hence their performance. While implementing speculation in modern design practice is errorprone
and mostly adhoc, this paper proposes a correctbyconstruction method for implementing speculation in Elastic Systems. The technique is based on applying provably correct transformations such as early
evaluation, insertion of antitokens and bubbles, retiming, and sharing. It allows to explore different microarchitectural solutions for better design tradeoffs. The benefits of speculation are illustrated with
two examples in which these transformations are systematically applied. The method proposed in this paper is amenable for automation in a synthesis flow.

Retiming and recycling for elastic systems with early evaluation
http://hdl.handle.net/2117/87917
Retiming and recycling for elastic systems with early evaluation
Bufistov, Dmitry; Cortadella Fortuny, Jordi; Galcerán Oms, Marc; Julvez Bueno, Jorge Emilio; Kishinevsky, Mike
Retiming and recycling are two transformations used to optimize the performance of latencyinsensitive (a.k.a. synchronous elastic) systems. This paper presents an approach that combines these two transformations for performance optimization of elastic systems with early evaluation. The method is based on Mixed Integer Linear Programming. On a set of random benchmarks the proposed method achieves, in average, 14.5% performance improvement over mindelay retiming configurations.
20160613T08:59:50Z
Bufistov, Dmitry
Cortadella Fortuny, Jordi
Galcerán Oms, Marc
Julvez Bueno, Jorge Emilio
Kishinevsky, Mike
Retiming and recycling are two transformations used to optimize the performance of latencyinsensitive (a.k.a. synchronous elastic) systems. This paper presents an approach that combines these two transformations for performance optimization of elastic systems with early evaluation. The method is based on Mixed Integer Linear Programming. On a set of random benchmarks the proposed method achieves, in average, 14.5% performance improvement over mindelay retiming configurations.

Divideandconquer strategies for process mining
http://hdl.handle.net/2117/87625
Divideandconquer strategies for process mining
Carmona Vargas, Josep; Cortadella Fortuny, Jordi; Kishinevsky, Mike
The main goal of Process Mining is to extract process models from logs of a system. Among the possible models to represent a process, Petri nets is an ideal candidate due to its graphical representation, clear semantics and expressive p ower. The theory of regions can be used to transform a log into a Petri net, but unfortunately the transformation requires algorithms with high complexity. This paper provides techniques to overcome this limitation. Either by using decomposition techniques, or by clustering events in the log and working on projections, the proposed techniques can be used to alleviat e the complexity and make the theory of regions practical for reallife problems.
A previous version of this report was titled "A recursive approach for Process Mining"
20160602T07:43:25Z
Carmona Vargas, Josep
Cortadella Fortuny, Jordi
Kishinevsky, Mike
The main goal of Process Mining is to extract process models from logs of a system. Among the possible models to represent a process, Petri nets is an ideal candidate due to its graphical representation, clear semantics and expressive p ower. The theory of regions can be used to transform a log into a Petri net, but unfortunately the transformation requires algorithms with high complexity. This paper provides techniques to overcome this limitation. Either by using decomposition techniques, or by clustering events in the log and working on projections, the proposed techniques can be used to alleviat e the complexity and make the theory of regions practical for reallife problems.

Analysis of the strategy "Hiring above the alphaquantile"
http://hdl.handle.net/2117/87542
Analysis of the strategy "Hiring above the alphaquantile"
Helmiy, Ahmed; Martínez Parra, Conrado; Panholzer, Alois
We study here the strategy hiring above the αquantile of the hired staﬀ. This strategy was introduced ﬁrst by Archibald and Martınez in 2009. We show here more results like lower and upper bounds for many interesting quantities for the general case, i.e., 0 < alpha < 1. For the main parameter, number of hired candidates, we were able to obtain the exact and limiting distributions for alpha = 1/d, with d a positive integer.
20160531T11:53:08Z
Helmiy, Ahmed
Martínez Parra, Conrado
Panholzer, Alois
We study here the strategy hiring above the αquantile of the hired staﬀ. This strategy was introduced ﬁrst by Archibald and Martınez in 2009. We show here more results like lower and upper bounds for many interesting quantities for the general case, i.e., 0 < alpha < 1. For the main parameter, number of hired candidates, we were able to obtain the exact and limiting distributions for alpha = 1/d, with d a positive integer.

A review on DISC 2005, the 19th International Symposium on Distributed Computing
http://hdl.handle.net/2117/87343
A review on DISC 2005, the 19th International Symposium on Distributed Computing
Blesa Aguilera, Maria Josep; Georgiou, Chryssis
DISC is an international symposium on the theory, design, analysis, implementation and application of distributed systems and networks. The wellknown International Symposium on Distributed Computing is organized annually in cooperation with the European Association for Theoretical Computer Science (EATCS). This is a review on the 19th International Symposium on Distributed Computing, which took place in Kraków, Poland, on September 2629, 2005. The proceedings of DISC 2005 are published by Springer, as volume 3724 of the Lecture Notes in Computer Science (LNCS) series. The conference website can be found at www.mimuw.edu.pl/~disc2005.
20160526T08:10:28Z
Blesa Aguilera, Maria Josep
Georgiou, Chryssis
DISC is an international symposium on the theory, design, analysis, implementation and application of distributed systems and networks. The wellknown International Symposium on Distributed Computing is organized annually in cooperation with the European Association for Theoretical Computer Science (EATCS). This is a review on the 19th International Symposium on Distributed Computing, which took place in Kraków, Poland, on September 2629, 2005. The proceedings of DISC 2005 are published by Springer, as volume 3724 of the Lecture Notes in Computer Science (LNCS) series. The conference website can be found at www.mimuw.edu.pl/~disc2005.