Articles de revista
http://hdl.handle.net/2117/3093
Wed, 29 Mar 2017 01:26:27 GMT2017-03-29T01:26:27ZThe HOM problem is EXPTIME-complete
http://hdl.handle.net/2117/102817
The HOM problem is EXPTIME-complete
Creus López, Carles; Gascon Caro, Adrian; Godoy Balil, Guillem; Ramos Garrido, Lander
We define a new class of tree automata with constraints and prove decidability of the emptiness problem for this class in exponential time. As a consequence, we obtain several EXPTIME-completeness results for problems on images of regular tree languages under tree homomorphisms, like set inclusion, regularity (HOM problem), and finiteness of set difference. Our result also has implications in term rewriting, since the set of reducible terms of a term rewrite system can be described as the image of a tree homomorphism. In particular, we prove that inclusion of sets of normal forms of term rewrite systems can be decided in exponential time. Analogous consequences arise in the context of XML typechecking, since types are defined by tree automata and some type transformations are homomorphic.
Thu, 23 Mar 2017 09:26:34 GMThttp://hdl.handle.net/2117/1028172017-03-23T09:26:34ZCreus López, CarlesGascon Caro, AdrianGodoy Balil, GuillemRamos Garrido, LanderWe define a new class of tree automata with constraints and prove decidability of the emptiness problem for this class in exponential time. As a consequence, we obtain several EXPTIME-completeness results for problems on images of regular tree languages under tree homomorphisms, like set inclusion, regularity (HOM problem), and finiteness of set difference. Our result also has implications in term rewriting, since the set of reducible terms of a term rewrite system can be described as the image of a tree homomorphism. In particular, we prove that inclusion of sets of normal forms of term rewrite systems can be decided in exponential time. Analogous consequences arise in the context of XML typechecking, since types are defined by tree automata and some type transformations are homomorphic.Construct, Merge, Solve and Adapt: Application to the repetition-free longest common subsequence problem
http://hdl.handle.net/2117/102814
Construct, Merge, Solve and Adapt: Application to the repetition-free longest common subsequence problem
Blum, Christian; Blesa Aguilera, Maria Josep
In this paper we present the application of a recently proposed, general, algorithm for combinatorial optimization to the repetition-free longest common subsequence problem. The applied algorithm, which is labelled Construct, Merge, Solve & Adapt, generates sub-instances based on merging the solution components found in randomly constructed solutions. These sub-instances are subsequently solved by means of an exact solver. Moreover, the considered sub-instances are dynamically changing due to adding new solution components at each iteration, and removing existing solution components on the basis of indicators about their usefulness. The results of applying this algorithm to the repetition-free longest common subsequence problem show that the algorithm generally outperforms competing approaches from the literature. Moreover, they show that the algorithm is competitive with CPLEX for small and medium size problem instances, whereas it outperforms CPLEX for larger problem instances.
Thu, 23 Mar 2017 07:48:23 GMThttp://hdl.handle.net/2117/1028142017-03-23T07:48:23ZBlum, ChristianBlesa Aguilera, Maria JosepIn this paper we present the application of a recently proposed, general, algorithm for combinatorial optimization to the repetition-free longest common subsequence problem. The applied algorithm, which is labelled Construct, Merge, Solve & Adapt, generates sub-instances based on merging the solution components found in randomly constructed solutions. These sub-instances are subsequently solved by means of an exact solver. Moreover, the considered sub-instances are dynamically changing due to adding new solution components at each iteration, and removing existing solution components on the basis of indicators about their usefulness. The results of applying this algorithm to the repetition-free longest common subsequence problem show that the algorithm generally outperforms competing approaches from the literature. Moreover, they show that the algorithm is competitive with CPLEX for small and medium size problem instances, whereas it outperforms CPLEX for larger problem instances.On the stability of generalized second price auctions with budgets
http://hdl.handle.net/2117/101923
On the stability of generalized second price auctions with budgets
Díaz Cort, Josep; Giotis, Ioannis; Kirousis, Lefteris; Markakis, Evangelos; Serna Iglesias, María José
The Generalized Second Price (GSP) auction used typically to model sponsored search auctions does not include the notion of budget constraints, which is present in practice. Motivated by this, we introduce the different variants of GSP auctions that take budgets into account in natural ways. We examine their stability by focusing on the existence of Nash equilibria and envy-free assignments. We highlight the differences between these mechanisms and find that only some of them exhibit both notions of stability. This shows the importance of carefully picking the right mechanism to ensure stable outcomes in the presence of budgets.
Sat, 04 Mar 2017 12:43:43 GMThttp://hdl.handle.net/2117/1019232017-03-04T12:43:43ZDíaz Cort, JosepGiotis, IoannisKirousis, LefterisMarkakis, EvangelosSerna Iglesias, María JoséThe Generalized Second Price (GSP) auction used typically to model sponsored search auctions does not include the notion of budget constraints, which is present in practice. Motivated by this, we introduce the different variants of GSP auctions that take budgets into account in natural ways. We examine their stability by focusing on the existence of Nash equilibria and envy-free assignments. We highlight the differences between these mechanisms and find that only some of them exhibit both notions of stability. This shows the importance of carefully picking the right mechanism to ensure stable outcomes in the presence of budgets.Amalgamation of domain specific languages with behaviour
http://hdl.handle.net/2117/100652
Amalgamation of domain specific languages with behaviour
Duran, Francisco; Moreno Delgado, Antonio; Orejas Valdés, Fernando; Zschaler, Steffen
Domain-specific languages (DSLs) become more useful the more specific they are to a particular domain. The resulting need for developing a substantial number of DSLs can only be satisfied if DSL development can be made as efficient as possible. One way in which to address this challenge is by enabling the reuse of (partial) DSLs in the construction of new DSLs. Reuse of DSLs builds on two foundations: a notion of DSL composition and theoretical results ensuring the safeness of composing DSLs with respect to the semantics of the component DSLs.
Given a graph-grammar formalisation of DSLs, in this paper, we build on graph transformation system morphisms to define parameterised DSLs and their instantiation by an amalgamation construction. Results on the protection of the behaviour along the induced morphisms allow us to safely reuse and combine definitions of DSLs to build more complex ones. We illustrate our proposal in e-Motions for a DSL for production-line systems and three independent DSLs for describing non-functional properties, namely response time, throughput, and failure rate.
Wed, 08 Feb 2017 08:20:14 GMThttp://hdl.handle.net/2117/1006522017-02-08T08:20:14ZDuran, FranciscoMoreno Delgado, AntonioOrejas Valdés, FernandoZschaler, SteffenDomain-specific languages (DSLs) become more useful the more specific they are to a particular domain. The resulting need for developing a substantial number of DSLs can only be satisfied if DSL development can be made as efficient as possible. One way in which to address this challenge is by enabling the reuse of (partial) DSLs in the construction of new DSLs. Reuse of DSLs builds on two foundations: a notion of DSL composition and theoretical results ensuring the safeness of composing DSLs with respect to the semantics of the component DSLs.
Given a graph-grammar formalisation of DSLs, in this paper, we build on graph transformation system morphisms to define parameterised DSLs and their instantiation by an amalgamation construction. Results on the protection of the behaviour along the induced morphisms allow us to safely reuse and combine definitions of DSLs to build more complex ones. We illustrate our proposal in e-Motions for a DSL for production-line systems and three independent DSLs for describing non-functional properties, namely response time, throughput, and failure rate.Comparing MapReduce and pipeline implementations for counting triangles
http://hdl.handle.net/2117/100102
Comparing MapReduce and pipeline implementations for counting triangles
Pasarella Sánchez, Ana Edelmira; Vidal, Maria-Esther; Zoltan Torres, Ana Cristina
A common method to define a parallel solution for a computational problem consists in finding a way to use the Divide and Conquer paradigm in order to have processors acting on its own data and scheduled in a parallel fashion. MapReduce is a programming model that follows this paradigm, and allows for the definition of efficient solutions by both decomposing a problem into steps on subsets of the input data and combining the results of each step to produce final results. Albeit used for the implementation of a wide variety of computational problems, MapReduce performance can be negatively affected whenever the replication factor grows or the size of the input is larger than the resources available at each processor. In this paper we show an alternative approach to implement the Divide and Conquer paradigm, named dynamic pipeline. The main features of dynamic pipelines are illustrated on a parallel implementation of the well-known problem of counting triangles in a graph. This problem is especially interesting either when the input graph does not fit in memory or is dynamically generated. To evaluate the properties of pipeline, a dynamic pipeline of processes and an ad-hoc version of MapReduce are implemented in the language Go, exploiting its ability to deal with channels and spawned processes. An empirical evaluation is conducted on graphs of different topologies, sizes, and densities. Observed results suggest that dynamic pipelines allows for an efficient implementation of the problem of counting triangles in a graph, particularly, in dense and large graphs, drastically reducing the execution time with respect to the MapReduce implementation.
Thu, 26 Jan 2017 11:13:06 GMThttp://hdl.handle.net/2117/1001022017-01-26T11:13:06ZPasarella Sánchez, Ana EdelmiraVidal, Maria-EstherZoltan Torres, Ana CristinaA common method to define a parallel solution for a computational problem consists in finding a way to use the Divide and Conquer paradigm in order to have processors acting on its own data and scheduled in a parallel fashion. MapReduce is a programming model that follows this paradigm, and allows for the definition of efficient solutions by both decomposing a problem into steps on subsets of the input data and combining the results of each step to produce final results. Albeit used for the implementation of a wide variety of computational problems, MapReduce performance can be negatively affected whenever the replication factor grows or the size of the input is larger than the resources available at each processor. In this paper we show an alternative approach to implement the Divide and Conquer paradigm, named dynamic pipeline. The main features of dynamic pipelines are illustrated on a parallel implementation of the well-known problem of counting triangles in a graph. This problem is especially interesting either when the input graph does not fit in memory or is dynamically generated. To evaluate the properties of pipeline, a dynamic pipeline of processes and an ad-hoc version of MapReduce are implemented in the language Go, exploiting its ability to deal with channels and spawned processes. An empirical evaluation is conducted on graphs of different topologies, sizes, and densities. Observed results suggest that dynamic pipelines allows for an efficient implementation of the problem of counting triangles in a graph, particularly, in dense and large graphs, drastically reducing the execution time with respect to the MapReduce implementation.Narrow proofs may be maximally long
http://hdl.handle.net/2117/99737
Narrow proofs may be maximally long
Atserias, Albert; Lauria, Massimo; Nordström, Jakob
We prove that there are 3-CNF formulas over n variables that can be refuted in resolution in width w but require resolution proofs of size n(Omega(w)). This shows that the simple counting argument that any formula refutable in width w must have a proof in size n(O(w)) is essentially tight. Moreover, our lower bound generalizes to polynomial calculus resolution and Sherali-Adams, implying that the corresponding size upper bounds in terms of degree and rank are tight as well. The lower bound does not extend all the way to Lasserre, however, since we show that there the formulas we study have proofs of constant rank and size polynomial in both n and w.
Fri, 20 Jan 2017 08:41:23 GMThttp://hdl.handle.net/2117/997372017-01-20T08:41:23ZAtserias, AlbertLauria, MassimoNordström, JakobWe prove that there are 3-CNF formulas over n variables that can be refuted in resolution in width w but require resolution proofs of size n(Omega(w)). This shows that the simple counting argument that any formula refutable in width w must have a proof in size n(O(w)) is essentially tight. Moreover, our lower bound generalizes to polynomial calculus resolution and Sherali-Adams, implying that the corresponding size upper bounds in terms of degree and rank are tight as well. The lower bound does not extend all the way to Lasserre, however, since we show that there the formulas we study have proofs of constant rank and size polynomial in both n and w.Firefighting as a strategic game
http://hdl.handle.net/2117/99674
Firefighting as a strategic game
Álvarez Faura, M. del Carme; Blesa Aguilera, Maria Josep; Molter, Hendrik
The Firefighter Problem was proposed in 1995 as a deterministic discrete-time model for the spread and containment of a fire. The problem is defined on an undirected finite graph G = (V, E), where fire breaks out initially at f nodes. In each subsequent time-step, two actions occur: a certain number b of firefighters are placed on nonburning nodes, permanently protecting them from the fire, then the fire spreads to all nondefended neighbors of the nodes on fire. Because the graph is finite, at some point each node is either on fire or saved, and thus the fire cannot spread further. One of the objectives for the problem is to place the firefighters in such a way that the number of saved nodes is maximized. The applications of the Firefighter Problem reach from real fires to the spreading of diseases and the containment of floods. Furthermore, it can be used to model the spread of computer viruses or viral marketing in communication networks. Most research on the problem considers the case in which the fire starts in a single place (i.e., f = 1), and in which the budget of available firefighters per time-step is one (i.e., b = 1). So does the work in this study. This configuration already leads to hard problems and, even in this case, the problem is known to be NP-hard. In this work, we study the problem from a game-theoretical perspective. We introduce a strategic game model for the Firefighter Problem to tackle its complexity from a different angle. We refer to it as the Firefighter Game. Such a game-based context seems very appropriate when applied to large networks where entities may act and make decisions based on their own interests, without global coordination. At every time-step of the game, a player decides whether to place a new firefighter in a nonburning node of the graph. If so, he must decide where to place it. By placing it, the player is indirectly deciding which nodes to protect at that time-step. We define different utility functions in order to model selfish and nonselfish scenarios, which lead to equivalent games. We show that the Price of Anarchy (PoA) is linear for a particular family of graphs, but it is at most two for trees. We also analyze the quality of the equilibria when coalitions among players are allowed. It turns out that it is possible to compute an equilibrium in polynomial time, even for constant-size coalitions. This yields to a polynomial time approximation algorithm for the problem and its approximation ratio equals the PoA of the corresponding game. We show that for some specific topologies, the PoA is constant when constant-size coalitions are considered.
Thu, 19 Jan 2017 12:21:27 GMThttp://hdl.handle.net/2117/996742017-01-19T12:21:27ZÁlvarez Faura, M. del CarmeBlesa Aguilera, Maria JosepMolter, HendrikThe Firefighter Problem was proposed in 1995 as a deterministic discrete-time model for the spread and containment of a fire. The problem is defined on an undirected finite graph G = (V, E), where fire breaks out initially at f nodes. In each subsequent time-step, two actions occur: a certain number b of firefighters are placed on nonburning nodes, permanently protecting them from the fire, then the fire spreads to all nondefended neighbors of the nodes on fire. Because the graph is finite, at some point each node is either on fire or saved, and thus the fire cannot spread further. One of the objectives for the problem is to place the firefighters in such a way that the number of saved nodes is maximized. The applications of the Firefighter Problem reach from real fires to the spreading of diseases and the containment of floods. Furthermore, it can be used to model the spread of computer viruses or viral marketing in communication networks. Most research on the problem considers the case in which the fire starts in a single place (i.e., f = 1), and in which the budget of available firefighters per time-step is one (i.e., b = 1). So does the work in this study. This configuration already leads to hard problems and, even in this case, the problem is known to be NP-hard. In this work, we study the problem from a game-theoretical perspective. We introduce a strategic game model for the Firefighter Problem to tackle its complexity from a different angle. We refer to it as the Firefighter Game. Such a game-based context seems very appropriate when applied to large networks where entities may act and make decisions based on their own interests, without global coordination. At every time-step of the game, a player decides whether to place a new firefighter in a nonburning node of the graph. If so, he must decide where to place it. By placing it, the player is indirectly deciding which nodes to protect at that time-step. We define different utility functions in order to model selfish and nonselfish scenarios, which lead to equivalent games. We show that the Price of Anarchy (PoA) is linear for a particular family of graphs, but it is at most two for trees. We also analyze the quality of the equilibria when coalitions among players are allowed. It turns out that it is possible to compute an equilibrium in polynomial time, even for constant-size coalitions. This yields to a polynomial time approximation algorithm for the problem and its approximation ratio equals the PoA of the corresponding game. We show that for some specific topologies, the PoA is constant when constant-size coalitions are considered.Celebrity games
http://hdl.handle.net/2117/98737
Celebrity games
Álvarez Faura, M. del Carme; Blesa Aguilera, Maria Josep; Duch Brown, Amalia; Messegué Buisan, Arnau; Serna Iglesias, María José
We introduce Celebrity games, a new model of network creation games. In this model players have weights (W being the sum of all the player's weights) and there is a critical distance ß as well as a link cost a. The cost incurred by a player depends on the cost of establishing links to other players and on the sum of the weights of those players that remain farther than the critical distance. Intuitively, the aim of any player is to be relatively close (at a distance less than ß ) from the rest of players, mainly of those having high weights. The main features of celebrity games are that: computing the best response of a player is NP-hard if ß>1 and polynomial time solvable otherwise; they always have a pure Nash equilibrium; the family of celebrity games having a connected Nash equilibrium is characterized (the so called star celebrity games) and bounds on the diameter of the resulting equilibrium graphs are given; a special case of star celebrity games shares its set of Nash equilibrium profiles with the MaxBD games with uniform bounded distance ß introduced in Bilò et al. [6]. Moreover, we analyze the Price of Anarchy (PoA) and of Stability (PoS) of celebrity games and give several bounds. These are that: for non-star celebrity games PoA=PoS=max{1,W/a}; for star celebrity games PoS=1 and PoA=O(min{n/ß,Wa}) but if the Nash Equilibrium is a tree then the PoA is O(1); finally, when ß=1 the PoA is at most 2. The upper bounds on the PoA are complemented with some lower bounds for ß=2.
Thu, 22 Dec 2016 07:35:11 GMThttp://hdl.handle.net/2117/987372016-12-22T07:35:11ZÁlvarez Faura, M. del CarmeBlesa Aguilera, Maria JosepDuch Brown, AmaliaMessegué Buisan, ArnauSerna Iglesias, María JoséWe introduce Celebrity games, a new model of network creation games. In this model players have weights (W being the sum of all the player's weights) and there is a critical distance ß as well as a link cost a. The cost incurred by a player depends on the cost of establishing links to other players and on the sum of the weights of those players that remain farther than the critical distance. Intuitively, the aim of any player is to be relatively close (at a distance less than ß ) from the rest of players, mainly of those having high weights. The main features of celebrity games are that: computing the best response of a player is NP-hard if ß>1 and polynomial time solvable otherwise; they always have a pure Nash equilibrium; the family of celebrity games having a connected Nash equilibrium is characterized (the so called star celebrity games) and bounds on the diameter of the resulting equilibrium graphs are given; a special case of star celebrity games shares its set of Nash equilibrium profiles with the MaxBD games with uniform bounded distance ß introduced in Bilò et al. [6]. Moreover, we analyze the Price of Anarchy (PoA) and of Stability (PoS) of celebrity games and give several bounds. These are that: for non-star celebrity games PoA=PoS=max{1,W/a}; for star celebrity games PoS=1 and PoA=O(min{n/ß,Wa}) but if the Nash Equilibrium is a tree then the PoA is O(1); finally, when ß=1 the PoA is at most 2. The upper bounds on the PoA are complemented with some lower bounds for ß=2.Network formation for asymmetric players and bilateral contracting
http://hdl.handle.net/2117/98314
Network formation for asymmetric players and bilateral contracting
Álvarez Faura, M. del Carme; Serna Iglesias, María José; Fernández, Aleix
We study a network formation game where players wish to send traffic to other players. Players can be seen as nodes of an undirected graph whose edges are defined by contracts between the corresponding players. Each player can contract bilaterally with others to form bidirectional links or break unilaterally contracts to eliminate the corresponding links. Our model is an extension of the traffic routing model considered in Arcaute, E., Johari, R., Mannor, S., (IEEE Trans. Automat. Contr. 54(8), 1765–1778 2009) in which we do not require the traffic to be uniform and all-to-all. Player i specifies the amount of traffic tij = 0 that wants to send to player j. Our notion of stability is the network pairwise Nash stability, when no node wishes to deviate unilaterally and no pair of nodes can obtain benefit from deviating bilaterally. We show a characterization of the topologies that are pairwise Nash stable for a given traffic matrix. We prove that the best response problem is NP-hard and devise a myopic dynamics so that the deviation of the active node can be computed in polynomial time. We show the convergence of the dynamics to pairwise Nash configurations, when the contracting functions are anti-symmetric and affine, and that the expected convergence time is polynomial in the number of nodes when the node activation process is uniform.
Thu, 15 Dec 2016 09:45:05 GMThttp://hdl.handle.net/2117/983142016-12-15T09:45:05ZÁlvarez Faura, M. del CarmeSerna Iglesias, María JoséFernández, AleixWe study a network formation game where players wish to send traffic to other players. Players can be seen as nodes of an undirected graph whose edges are defined by contracts between the corresponding players. Each player can contract bilaterally with others to form bidirectional links or break unilaterally contracts to eliminate the corresponding links. Our model is an extension of the traffic routing model considered in Arcaute, E., Johari, R., Mannor, S., (IEEE Trans. Automat. Contr. 54(8), 1765–1778 2009) in which we do not require the traffic to be uniform and all-to-all. Player i specifies the amount of traffic tij = 0 that wants to send to player j. Our notion of stability is the network pairwise Nash stability, when no node wishes to deviate unilaterally and no pair of nodes can obtain benefit from deviating bilaterally. We show a characterization of the topologies that are pairwise Nash stable for a given traffic matrix. We prove that the best response problem is NP-hard and devise a myopic dynamics so that the deviation of the active node can be computed in polynomial time. We show the convergence of the dynamics to pairwise Nash configurations, when the contracting functions are anti-symmetric and affine, and that the expected convergence time is polynomial in the number of nodes when the node activation process is uniform.Dimension and codimension of simple games
http://hdl.handle.net/2117/97660
Dimension and codimension of simple games
Kurz, Sascha; Molinero Albareda, Xavier; Olsen, Martin; Serna Iglesias, María José
This paper studies the complexity of computing a representation of a simple game as the intersection (union) of weighted majority games, as well as, the dimension or the codimension. We also present some examples with linear dimension and exponential codimension with respect to the number of players.
Thu, 01 Dec 2016 18:56:01 GMThttp://hdl.handle.net/2117/976602016-12-01T18:56:01ZKurz, SaschaMolinero Albareda, XavierOlsen, MartinSerna Iglesias, María JoséThis paper studies the complexity of computing a representation of a simple game as the intersection (union) of weighted majority games, as well as, the dimension or the codimension. We also present some examples with linear dimension and exponential codimension with respect to the number of players.