Reports de recerca
http://hdl.handle.net/2117/3094
Mon, 16 Jan 2017 17:44:45 GMT2017-01-16T17:44:45ZFringe analysis of synchronized parallel algorithms on 2--3 trees
http://hdl.handle.net/2117/98212
Fringe analysis of synchronized parallel algorithms on 2--3 trees
Baeza-Yates, R; Gabarró Vallès, Joaquim; Messeguer Peypoch, Xavier
We are interested in the fringe analysis of synchronized parallel insertion algorithms on 2—3 trees namely the algorithm of W.Paul
U. Vishkin and H. Wagener PVW. This algorithm inserts k keys into
a tree of size n with parallel time Olog n log k
Fringe analysis studies the distribution of the bottom subtrees and it is
still an open problem for parallel algorithms on search trees. To tackle
this problem we introduce a new kind of algorithms whose two extreme
cases seems to upper and lower bounds the performance of the PVW
algorithm.
We extend the fringe analysis to parallel algorithms and we get a rich
mathematical structure giving new interpretations even in the sequential
case. The process of insertions is modeled by a Markov chain and the
coecients of the transition matrix are related with the expected local
behavior of our algorithm. Finally we show that this matrix has a power
expansion over (n+1)-1 where the coecients are the binomial transform
of the expected local behavior. This expansion shows that the parallel
case can be approximated by iterating the sequential case.
Wed, 14 Dec 2016 13:10:05 GMThttp://hdl.handle.net/2117/982122016-12-14T13:10:05ZBaeza-Yates, RGabarró Vallès, JoaquimMesseguer Peypoch, XavierWe are interested in the fringe analysis of synchronized parallel insertion algorithms on 2—3 trees namely the algorithm of W.Paul
U. Vishkin and H. Wagener PVW. This algorithm inserts k keys into
a tree of size n with parallel time Olog n log k
Fringe analysis studies the distribution of the bottom subtrees and it is
still an open problem for parallel algorithms on search trees. To tackle
this problem we introduce a new kind of algorithms whose two extreme
cases seems to upper and lower bounds the performance of the PVW
algorithm.
We extend the fringe analysis to parallel algorithms and we get a rich
mathematical structure giving new interpretations even in the sequential
case. The process of insertions is modeled by a Markov chain and the
coecients of the transition matrix are related with the expected local
behavior of our algorithm. Finally we show that this matrix has a power
expansion over (n+1)-1 where the coecients are the binomial transform
of the expected local behavior. This expansion shows that the parallel
case can be approximated by iterating the sequential case.Simple and efficient tree comparison
http://hdl.handle.net/2117/97629
Simple and efficient tree comparison
Valiente Feruglio, Gabriel Alejandro
A new distance metric for rooted trees is presented which is based on
the largest common forest of two rooted trees. The new measure is
superior to previous measures based on tree edit distance, because no
particular tree edit operations together with their costs or weights
need to be defined. The
metric can be computed in expected time linear in the number of nodes,
on rooted trees of unbounded degree, either unordered or ordered,
labeled or unlabeled. An algorithm for computing the metric is given
which is based on a simple and efficient bottom-up algorithm for finding
all common rooted subtrees in a forest.
Thu, 01 Dec 2016 15:09:22 GMThttp://hdl.handle.net/2117/976292016-12-01T15:09:22ZValiente Feruglio, Gabriel AlejandroA new distance metric for rooted trees is presented which is based on
the largest common forest of two rooted trees. The new measure is
superior to previous measures based on tree edit distance, because no
particular tree edit operations together with their costs or weights
need to be defined. The
metric can be computed in expected time linear in the number of nodes,
on rooted trees of unbounded degree, either unordered or ordered,
labeled or unlabeled. An algorithm for computing the metric is given
which is based on a simple and efficient bottom-up algorithm for finding
all common rooted subtrees in a forest.Tree edit distance and common subtrees
http://hdl.handle.net/2117/97554
Tree edit distance and common subtrees
Valiente Feruglio, Gabriel Alejandro
The relationship between tree edit distance and maximum common
subtrees is established, showing that a tree edit distance constrained
by insertion and deletions on leaves only and by a simple condition on
the cost of the tree edit operations, corresponds to a maximum commonsubtree isomorphism, allowing thus the use of known tree edit distance algorithms to solve the maximum common subtree problem, and viceversa. Further, a tree distance based on the size of a maximum common subtree is introduced.
Wed, 30 Nov 2016 16:31:58 GMThttp://hdl.handle.net/2117/975542016-11-30T16:31:58ZValiente Feruglio, Gabriel AlejandroThe relationship between tree edit distance and maximum common
subtrees is established, showing that a tree edit distance constrained
by insertion and deletions on leaves only and by a simple condition on
the cost of the tree edit operations, corresponds to a maximum commonsubtree isomorphism, allowing thus the use of known tree edit distance algorithms to solve the maximum common subtree problem, and viceversa. Further, a tree distance based on the size of a maximum common subtree is introduced.Exponential speedup of fixed parameter algorithms on K_{3,3}-minor-free or K_{5}-minor-free graphs
http://hdl.handle.net/2117/97525
Exponential speedup of fixed parameter algorithms on K_{3,3}-minor-free or K_{5}-minor-free graphs
Hajiaghayi, Mohammad Taghi; Demaine, Erik D.; Thilikos Touloupas, Dimitrios
We present a fixed parameter algorithm that constructively solves the
k-dominating set problem on graphs excluding one of the K_{5} or
K_3,3 as a minor in time O(3^{6sqrt{34 k}}n^{O(1)}). In fact,
we present our algorithm for any H-minor-free graph where H is
a single-crossing graph (can be drawn on the plane with at most one
crossing) and obtain the algorithm for K_{3,3} (K_{5})-minor-free
graphs as a special case. As a consequence, we extend our results to
several other problems such as vertex cover, edge dominating set,
independent set, clique-transversal set, kernels in digraphs,
feedback vertex set and a series of vertex removal problems.
Our work generalizes and extends the recent result of exponential speedup
in designing fixed-parameter algorithms on planar
graphs due to Alber et al. to other (non-planar) classes of graphs.
Wed, 30 Nov 2016 14:35:59 GMThttp://hdl.handle.net/2117/975252016-11-30T14:35:59ZHajiaghayi, Mohammad TaghiDemaine, Erik D.Thilikos Touloupas, DimitriosWe present a fixed parameter algorithm that constructively solves the
k-dominating set problem on graphs excluding one of the K_{5} or
K_3,3 as a minor in time O(3^{6sqrt{34 k}}n^{O(1)}). In fact,
we present our algorithm for any H-minor-free graph where H is
a single-crossing graph (can be drawn on the plane with at most one
crossing) and obtain the algorithm for K_{3,3} (K_{5})-minor-free
graphs as a special case. As a consequence, we extend our results to
several other problems such as vertex cover, edge dominating set,
independent set, clique-transversal set, kernels in digraphs,
feedback vertex set and a series of vertex removal problems.
Our work generalizes and extends the recent result of exponential speedup
in designing fixed-parameter algorithms on planar
graphs due to Alber et al. to other (non-planar) classes of graphs.Classes of term rewrite systems with polynomial confluence problems
http://hdl.handle.net/2117/97487
Classes of term rewrite systems with polynomial confluence problems
Godoy Balil, Guillem; Nieuwenhuis, Robert Lukas Mario
The confluence property of ground (i.e., variable-free) term rewrite
systems (GTRS) is well-known to be decidable.
This was proved independently in [DTHL87,DHLT90]
and in [Oya87] using tree automata techniques and
ground tree transducer techniques (originated from this problem),
yielding EXPTIME decision procedures (PSPACE for strings). Since
then, it has been a well-known longstanding open question whether this
bound is optimal (see, e.g., [RTA01]).
In [CGN01] we gave the first polynomial-time algorithm for
deciding the confluence of GTRS. Later in [Tiw02] this result was
extended, using abstract congruent closure techniques, to linear-shallow TRS.
Here, we give a new and much simpler proof of the latter result.
Wed, 30 Nov 2016 09:59:06 GMThttp://hdl.handle.net/2117/974872016-11-30T09:59:06ZGodoy Balil, GuillemNieuwenhuis, Robert Lukas MarioThe confluence property of ground (i.e., variable-free) term rewrite
systems (GTRS) is well-known to be decidable.
This was proved independently in [DTHL87,DHLT90]
and in [Oya87] using tree automata techniques and
ground tree transducer techniques (originated from this problem),
yielding EXPTIME decision procedures (PSPACE for strings). Since
then, it has been a well-known longstanding open question whether this
bound is optimal (see, e.g., [RTA01]).
In [CGN01] we gave the first polynomial-time algorithm for
deciding the confluence of GTRS. Later in [Tiw02] this result was
extended, using abstract congruent closure techniques, to linear-shallow TRS.
Here, we give a new and much simpler proof of the latter result.A Random graph model for optical networks of sensors
http://hdl.handle.net/2117/97399
A Random graph model for optical networks of sensors
Díaz Cort, Josep; Petit Silvestre, Jordi; Serna Iglesias, María José
In this paper we propose a model for Smart Dust Networks and show its applicability when the goal of the network is monitoring an area under the surveillance of a base station. We analyze basic parameters of these nets and simple distributed protocols. These protocols provide a communication layer for networks of sensors that communicate through optical links.
Tue, 29 Nov 2016 11:24:32 GMThttp://hdl.handle.net/2117/973992016-11-29T11:24:32ZDíaz Cort, JosepPetit Silvestre, JordiSerna Iglesias, María JoséIn this paper we propose a model for Smart Dust Networks and show its applicability when the goal of the network is monitoring an area under the surveillance of a base station. We analyze basic parameters of these nets and simple distributed protocols. These protocols provide a communication layer for networks of sensors that communicate through optical links.Bounds on the max and min bisection of random cubic and 4-regular graphs
http://hdl.handle.net/2117/97396
Bounds on the max and min bisection of random cubic and 4-regular graphs
Díaz Cort, Josep; Do, Norman; Serna Iglesias, María José; Wormald, Nick
In this paper we present simple randomized algorithms to bisect
cubic and 4-regular graphs. These algorithms produce bisections of
size
asymptotically at most
0.17404n for typical random cubic n-vertex graphs, and n/3+eps n for
random 4-regular (any eps>0).
We also obtain asymptotic
lower bounds for the size of the maximum bisection, for random cubic and
random 4-regular graphs with $ vertices,
of 1.32697 n and 5n/3+eps n, respectively. In all cases
except the minimum bisection of cubic graphs, these give new results on
the
existence of regular graphs with small or large bisections. The
randomized
algorithms are derived from a greedy algorithm and the analysis is
based on the differential equation method.
Tue, 29 Nov 2016 11:05:05 GMThttp://hdl.handle.net/2117/973962016-11-29T11:05:05ZDíaz Cort, JosepDo, NormanSerna Iglesias, María JoséWormald, NickIn this paper we present simple randomized algorithms to bisect
cubic and 4-regular graphs. These algorithms produce bisections of
size
asymptotically at most
0.17404n for typical random cubic n-vertex graphs, and n/3+eps n for
random 4-regular (any eps>0).
We also obtain asymptotic
lower bounds for the size of the maximum bisection, for random cubic and
random 4-regular graphs with $ vertices,
of 1.32697 n and 5n/3+eps n, respectively. In all cases
except the minimum bisection of cubic graphs, these give new results on
the
existence of regular graphs with small or large bisections. The
randomized
algorithms are derived from a greedy algorithm and the analysis is
based on the differential equation method.Where should concurrent rotations take place to rebalance a distributed arbitrary search tree?
http://hdl.handle.net/2117/97310
Where should concurrent rotations take place to rebalance a distributed arbitrary search tree?
Bougé, Luc; Gabarró Vallès, Joaquim; Messeguer Peypoch, Xavier
We address the concurrent insertion and deletion of keys in binary almost balanced search trees (AVL trees). We show that this problem can be studied through the self-reorganization of distributed systems of processes controlled by local evolution rules in the line of the approach of Dijkstra and Scholten. In particular, we show that our approach encapsulates a number of previous attempts described in the literature. This solves in a very general setting an old question raised by H.T. Kung and P.L. Lehman: where should rotations take place to rebalance arbitrary trees?
Mon, 28 Nov 2016 12:30:28 GMThttp://hdl.handle.net/2117/973102016-11-28T12:30:28ZBougé, LucGabarró Vallès, JoaquimMesseguer Peypoch, XavierWe address the concurrent insertion and deletion of keys in binary almost balanced search trees (AVL trees). We show that this problem can be studied through the self-reorganization of distributed systems of processes controlled by local evolution rules in the line of the approach of Dijkstra and Scholten. In particular, we show that our approach encapsulates a number of previous attempts described in the literature. This solves in a very general setting an old question raised by H.T. Kung and P.L. Lehman: where should rotations take place to rebalance arbitrary trees?Unranking of combinatorial structures
http://hdl.handle.net/2117/97301
Unranking of combinatorial structures
Molinero Albareda, Xavier
The present work is a study of the deterministic generation of
combinatorial structures. We generate classes of combinatorial
structures formally specifiable by grammars involving unlabelled
sequence, unlabelled set, unlabelled multiset, unlabelled pointing,
unlabelled unpointing, unlabelled substitution, labelled sequence,
labelled set, labelled multiset, labelled cycle, labelled pointing,
labelled unpointing and labelled substitution constructions.
It consists of some basic preliminaries about classes
of combinatorial structures and three chapters. The first
one, Unlabelled Unranking , solves the unranking of unlabelled
structures. The second one, Labelled
Unranking, solves the unranking of labelled
structures. The third one, Product of labellings,
explains the order of the labellings in the structures. Appendix
contains the libraries developed in this work.
Mon, 28 Nov 2016 10:45:06 GMThttp://hdl.handle.net/2117/973012016-11-28T10:45:06ZMolinero Albareda, XavierThe present work is a study of the deterministic generation of
combinatorial structures. We generate classes of combinatorial
structures formally specifiable by grammars involving unlabelled
sequence, unlabelled set, unlabelled multiset, unlabelled pointing,
unlabelled unpointing, unlabelled substitution, labelled sequence,
labelled set, labelled multiset, labelled cycle, labelled pointing,
labelled unpointing and labelled substitution constructions.
It consists of some basic preliminaries about classes
of combinatorial structures and three chapters. The first
one, Unlabelled Unranking , solves the unranking of unlabelled
structures. The second one, Labelled
Unranking, solves the unranking of labelled
structures. The third one, Product of labellings,
explains the order of the labellings in the structures. Appendix
contains the libraries developed in this work.The PgaFrame - a frame for parallel genetic algorithms
http://hdl.handle.net/2117/97280
The PgaFrame - a frame for parallel genetic algorithms
Petit Silvestre, Jordi
The PgaFrame offers to non-expert users the possibility to solve optimization problems via genetic algorithms on parallel computers.
This frame has appeared as the natural fusion of two different
projects: PgaPack and Frames. The PgaFrame combines the major features of these projects: it integrates the capabilities to specify genetic algorithms offered by the PgaPack library and the support of Frames to the easy and portable programming of parallel machines. In this way, a complex framework to develop genetic algorithms is achieved.
Mon, 28 Nov 2016 09:08:24 GMThttp://hdl.handle.net/2117/972802016-11-28T09:08:24ZPetit Silvestre, JordiThe PgaFrame offers to non-expert users the possibility to solve optimization problems via genetic algorithms on parallel computers.
This frame has appeared as the natural fusion of two different
projects: PgaPack and Frames. The PgaFrame combines the major features of these projects: it integrates the capabilities to specify genetic algorithms offered by the PgaPack library and the support of Frames to the easy and portable programming of parallel machines. In this way, a complex framework to develop genetic algorithms is achieved.