Cristóbal Camarero | Universidad de Cantabria (original) (raw)
Papers by Cristóbal Camarero
2008 International Conference on Field Programmable Logic and Applications, 2008
The SMILE project accelerates scientific and industrial applications by means of a cluster of low... more The SMILE project accelerates scientific and industrial applications by means of a cluster of low-cost FPGA boards. With this approach the intensive calculation tasks are accelerated using the FPGA logic, while the communication patterns of the applications remains unchanged by using a Message Passing Library over Linux. This paper explains the cluster architecture: the SMILE nodes and the developed high-speed communication network for the FPGA RocketIO interfaces. A SystemC model developed to simulate the cluster is also detailed. In order to show the potential of the SMILE proposal a Content-Based Information Retrieval parallel application has been developed and compared with a HP cluster architecture in terms of response time and power consumption.
2008 16th International Symposium on Field-Programmable Custom Computing Machines, 2008
Abstract The SMILE project attempts to build efficient lowcost clusters based on FPGA boards usin... more Abstract The SMILE project attempts to build efficient lowcost clusters based on FPGA boards using their reconfigurability capabilities. A real parallel application of Content-Based Information Retrieval over the SMILE cluster is presented. Using this application the SMILE cluster¿ s performance is evaluated and compared in terms of time and power consumption with traditional cluster architecture.
Journal of Symbolic Computation, 2010
A graph-based model of perfect two-dimensional codes is presented in this work. This model facili... more A graph-based model of perfect two-dimensional codes is presented in this work. This model facilitates the study of the metric properties of the codes. Signal spaces are modeled by means of Cayley graphs defined over the Gaussian integers and denoted as Gaussian graphs. Codewords of perfect codes will be represented by vertices of a quotient graph of the Gaussian graph in which the signal space has been defined. It will be shown that any quotient graph of a Gaussian graph is indeed a Gaussian graph. This makes it possible to apply previously known properties of Gaussian graphs to the analysis of perfect codes. To illustrate the modeling power of this graph-based tool, perfect Lee codes will be analyzed in terms of Gaussian graphs and their quotients.
Journal of Symbolic Computation, 2010
A graph-based model of perfect two-dimensional codes is presented in this work. This model facili... more A graph-based model of perfect two-dimensional codes is presented in this work. This model facilitates the study of the metric properties of the codes. Signal spaces are modeled by means of Cayley graphs defined over the Gaussian integers and denoted as Gaussian graphs. Codewords of perfect codes will be represented by vertices of a quotient graph of the Gaussian graph in which the signal space has been defined. It will be shown that any quotient graph of a Gaussian graph is indeed a Gaussian graph. This makes it possible to apply previously known properties of Gaussian graphs to the analysis of perfect codes. To illustrate the modeling power of this graph-based tool, perfect Lee codes will be analyzed in terms of Gaussian graphs and their quotients.
2008 IEEE International Symposium on Information Theory, 2008
Abstract In order to propose a new metric over QAM constellations, diagonal Gaussian graphs defin... more Abstract In order to propose a new metric over QAM constellations, diagonal Gaussian graphs defined over quotients of the Gaussian integers are introduced in this paper. Distance properties of the constellations are detailed by means of the vertex-to-vertex distribution of this family of graphs. Moreover, perfect codes for this metric are considered. Finally, notable subgraphs of diagonal Gaussian graphs are studied which leads to relate the proposed metric to other well-known graph-based metrics such as the Lee distance.
—In the late years many different interconnection networks have been used with two main tendencie... more —In the late years many different interconnection networks have been used with two main tendencies. One is characterized by the use of high-degree routers with long wires while the other uses routers of much smaller degree. The latter rely on two-dimensional mesh and torus topologies with shorter local links. This paper focuses on doubling the degree of common 2D meshes and tori while still preserving an attractive layout for VLSI design. By adding a set of diagonal links in one direction, diagonal networks are obtained. By adding a second set of links, networks of degree eight are built, named king networks. This research presents a comprehensive study of these networks which includes a topological analysis, the proposal of appropriate routing procedures and an empirical evaluation. King networks exhibit a number of attractive characteristics which translate to reduced execution times of parallel applications. For example, the execution times NPB suite are reduced up to a 30%. In addition, this work reveals other properties of king networks such as perfect partitioning that deserves further attention for its convenient exploitation in forthcoming high-performance parallel systems.
Lecture Notes in Computer Science, 2010
Abstract. In this paper we propose two new topologies for on-chip net-works that we have denoted ... more Abstract. In this paper we propose two new topologies for on-chip net-works that we have denoted as king mesh and king torus. These are a higher degree evolution of the classical mesh and torus topologies. In a king network packets can traverse the networks using orthogonal ...
ACM Transactions on Architecture and Code Optimization, 2014
Current HPC and datacenter networks rely on large-radix routers. Hamming graphs (Cartesian produc... more Current HPC and datacenter networks rely on large-radix routers. Hamming graphs (Cartesian products of complete graphs) and dragonflies (two-level direct networks with nodes organized in groups) are some direct topologies proposed for such networks. The original definition of the dragonfly topology is very loose, with several degrees of freedom such as the inter-and intra-group topology, the specific global connectivity and the number of parallel links between groups (or trunking level).
Proceedings of the 2013 Interconnection Network Architecture: On-Chip, Multi-Chip on - IMA-OCMC '13, 2013
ABSTRACT Dragonfly networks are composed of interconnected groups of routers. Adaptive routing al... more ABSTRACT Dragonfly networks are composed of interconnected groups of routers. Adaptive routing allows packets to be forwarded minimally or non-minimally adapting to the traffic conditions in the network. While minimal routing sends traffic directly between groups, non-minimal routing employs an intermediate group to balance network load. A random selection of this intermediate group (denoted as RRG) typically implies an extra local hop in the source group, what increases average path length and can reduce performance. In this paper we identify different policies for the selection of such intermediate group and explore their performance. Interestingly, simulation results show that an eager policy (denoted as CRG) that selects the intermediate group only between those directly connected to the ongoing router causes starvation in some network nodes. On the contrary, the best performance is obtained by a "mixed mode" policy (denoted as MM) that adds a local hop when the packet has moved away from the source router.
2008 IEEE International Symposium on Information Theory, 2008
Abstract In order to propose a new metric over QAM constellations, diagonal Gaussian graphs defin... more Abstract In order to propose a new metric over QAM constellations, diagonal Gaussian graphs defined over quotients of the Gaussian integers are introduced in this paper. Distance properties of the constellations are detailed by means of the vertex-to-vertex distribution of this family of graphs. Moreover, perfect codes for this metric are considered. Finally, notable subgraphs of diagonal Gaussian graphs are studied which leads to relate the proposed metric to other well-known graph-based metrics such as the Lee distance.
Advances in Mathematics of Communications, 2015
In this paper a wide family of identifying codes over regular Cayley graphs of degree four which ... more In this paper a wide family of identifying codes over regular Cayley graphs of degree four which are built over finite Abelian groups is presented. Some of the codes in this construction are also perfect. The graphs considered include some well-known graphs such as tori, twisted tori and Kronecker products of two cycles. Therefore, the codes can be used for identification in these graphs. Finally, an example of how these codes can be applied for adaptive identification over these graphs is presented.
IEEE Transactions on Parallel and Distributed Systems, 2015
Torus networks of moderate degree have been widely used in the supercomputer industry. Tori are s... more Torus networks of moderate degree have been widely used in the supercomputer industry. Tori are superb when used for executing applications that require near-neighbor communications. Nevertheless, they are not so good when dealing with global communications. Hence, typical 3D implementations have evolved to 5D networks, among other reasons, to reduce network distances. Most of these big systems are mixed-radix tori which are not the best option for minimizing distances and efficiently using network resources. This paper is focused on improving the topological properties of these networks.
The present work is devoted to characterize the family of symmetric undirected Cayley graphs over... more The present work is devoted to characterize the family of symmetric undirected Cayley graphs over finite Abelian groups for degrees 4 and 6. arXiv:1403.5440v1 [math.CO] From here onwards, all matrices will be considered to be non-singular, unless the contrary is stated. Note that, since Z n /M Z n has | det(M )| elements, this will be the number of nodes of Cay(Z n /M Z n ; ±B n ). Moreover, since any vertex v is adjacent to v ± e i (mod M ), Cay(Z n /M Z n ; ±B n ) is, in general, a regular graph of degree 2n, that is, any node has 2n different neighbours. Then, we call n the dimension of the graph. Note that when e i ≡ ±e j (mod M ) or 2e i ≡ 0 (mod M ) for some 1 ≤ i, j ≤ n then the degree of the Cayley graph is less than 2n. In that case we can also consider the corresponding multigraph, which always has degree 2n. The hypercube could be considered as an extreme case since ∀i ∈ {1, . . . , n}, 2e i ≡ 0 (mod M ) and therefore it has degree n.
A construction of 2-quasi-perfect Lee codes is given over the space Z n p for p prime, p ≡ ±5 (mo... more A construction of 2-quasi-perfect Lee codes is given over the space Z n p for p prime, p ≡ ±5 (mod 12) and n = 2[ p 4 ]. It is known that there are infinite such primes. Perfect codes for the Lee-metric were conjectured by Golomb and Welch not to exist, which has been proved for large radii and also for low dimension. The codes found are very close to be perfect, which tells about the nature of the conjecture. Some computations show that related graphs are Ramanujan, which could provide further connections between the fields.
The Journal of Supercomputing, 2014
2008 16th International Symposium on Field-Programmable Custom Computing Machines, 2008
Abstract The SMILE project attempts to build efficient lowcost clusters based on FPGA boards usin... more Abstract The SMILE project attempts to build efficient lowcost clusters based on FPGA boards using their reconfigurability capabilities. A real parallel application of Content-Based Information Retrieval over the SMILE cluster is presented. Using this application the SMILE cluster¿ s performance is evaluated and compared in terms of time and power consumption with traditional cluster architecture.
2012 IEEE 14th International Conference on High Performance Computing and Communication & 2012 IEEE 9th International Conference on Embedded Software and Systems, 2012
Abstract This paper analyzes the robustness of the king networks for fault tolerance. To this aim... more Abstract This paper analyzes the robustness of the king networks for fault tolerance. To this aim, a performance evaluation of two well known fault tolerant routing algorithms in king as well as 2d networks is done. Immunet that uses two virtual channels and Immucube, that has a better performance while requiring three virtual channels. Experimental results confirm the excellent behavior, both in performance and scalability, of the king topologies in the presence of failures. Finally, taking advantage of the topological features of king networks, ...
IEEE Transactions on Parallel and Distributed Systems, 2014
Torus networks of moderate degree have been widely used in the supercomputer industry. Tori are s... more Torus networks of moderate degree have been widely used in the supercomputer industry. Tori are superb when used for executing applications that require near-neighbor communications. Nevertheless, they are not so good when dealing with global communications. Hence, typical 3D implementations have evolved to 5D networks, among other reasons, to reduce network distances. Most of these big systems are mixed-radix tori, which are not the best option for minimizing distances and efficiently using network resources. This paper is focused on improving the topological properties of this kind of networks.
2008 International Conference on Field Programmable Logic and Applications, 2008
The SMILE project accelerates scientific and industrial applications by means of a cluster of low... more The SMILE project accelerates scientific and industrial applications by means of a cluster of low-cost FPGA boards. With this approach the intensive calculation tasks are accelerated using the FPGA logic, while the communication patterns of the applications remains unchanged by using a Message Passing Library over Linux. This paper explains the cluster architecture: the SMILE nodes and the developed high-speed
2008 International Conference on Field Programmable Logic and Applications, 2008
The SMILE project accelerates scientific and industrial applications by means of a cluster of low... more The SMILE project accelerates scientific and industrial applications by means of a cluster of low-cost FPGA boards. With this approach the intensive calculation tasks are accelerated using the FPGA logic, while the communication patterns of the applications remains unchanged by using a Message Passing Library over Linux. This paper explains the cluster architecture: the SMILE nodes and the developed high-speed communication network for the FPGA RocketIO interfaces. A SystemC model developed to simulate the cluster is also detailed. In order to show the potential of the SMILE proposal a Content-Based Information Retrieval parallel application has been developed and compared with a HP cluster architecture in terms of response time and power consumption.
2008 16th International Symposium on Field-Programmable Custom Computing Machines, 2008
Abstract The SMILE project attempts to build efficient lowcost clusters based on FPGA boards usin... more Abstract The SMILE project attempts to build efficient lowcost clusters based on FPGA boards using their reconfigurability capabilities. A real parallel application of Content-Based Information Retrieval over the SMILE cluster is presented. Using this application the SMILE cluster¿ s performance is evaluated and compared in terms of time and power consumption with traditional cluster architecture.
Journal of Symbolic Computation, 2010
A graph-based model of perfect two-dimensional codes is presented in this work. This model facili... more A graph-based model of perfect two-dimensional codes is presented in this work. This model facilitates the study of the metric properties of the codes. Signal spaces are modeled by means of Cayley graphs defined over the Gaussian integers and denoted as Gaussian graphs. Codewords of perfect codes will be represented by vertices of a quotient graph of the Gaussian graph in which the signal space has been defined. It will be shown that any quotient graph of a Gaussian graph is indeed a Gaussian graph. This makes it possible to apply previously known properties of Gaussian graphs to the analysis of perfect codes. To illustrate the modeling power of this graph-based tool, perfect Lee codes will be analyzed in terms of Gaussian graphs and their quotients.
Journal of Symbolic Computation, 2010
A graph-based model of perfect two-dimensional codes is presented in this work. This model facili... more A graph-based model of perfect two-dimensional codes is presented in this work. This model facilitates the study of the metric properties of the codes. Signal spaces are modeled by means of Cayley graphs defined over the Gaussian integers and denoted as Gaussian graphs. Codewords of perfect codes will be represented by vertices of a quotient graph of the Gaussian graph in which the signal space has been defined. It will be shown that any quotient graph of a Gaussian graph is indeed a Gaussian graph. This makes it possible to apply previously known properties of Gaussian graphs to the analysis of perfect codes. To illustrate the modeling power of this graph-based tool, perfect Lee codes will be analyzed in terms of Gaussian graphs and their quotients.
2008 IEEE International Symposium on Information Theory, 2008
Abstract In order to propose a new metric over QAM constellations, diagonal Gaussian graphs defin... more Abstract In order to propose a new metric over QAM constellations, diagonal Gaussian graphs defined over quotients of the Gaussian integers are introduced in this paper. Distance properties of the constellations are detailed by means of the vertex-to-vertex distribution of this family of graphs. Moreover, perfect codes for this metric are considered. Finally, notable subgraphs of diagonal Gaussian graphs are studied which leads to relate the proposed metric to other well-known graph-based metrics such as the Lee distance.
—In the late years many different interconnection networks have been used with two main tendencie... more —In the late years many different interconnection networks have been used with two main tendencies. One is characterized by the use of high-degree routers with long wires while the other uses routers of much smaller degree. The latter rely on two-dimensional mesh and torus topologies with shorter local links. This paper focuses on doubling the degree of common 2D meshes and tori while still preserving an attractive layout for VLSI design. By adding a set of diagonal links in one direction, diagonal networks are obtained. By adding a second set of links, networks of degree eight are built, named king networks. This research presents a comprehensive study of these networks which includes a topological analysis, the proposal of appropriate routing procedures and an empirical evaluation. King networks exhibit a number of attractive characteristics which translate to reduced execution times of parallel applications. For example, the execution times NPB suite are reduced up to a 30%. In addition, this work reveals other properties of king networks such as perfect partitioning that deserves further attention for its convenient exploitation in forthcoming high-performance parallel systems.
Lecture Notes in Computer Science, 2010
Abstract. In this paper we propose two new topologies for on-chip net-works that we have denoted ... more Abstract. In this paper we propose two new topologies for on-chip net-works that we have denoted as king mesh and king torus. These are a higher degree evolution of the classical mesh and torus topologies. In a king network packets can traverse the networks using orthogonal ...
ACM Transactions on Architecture and Code Optimization, 2014
Current HPC and datacenter networks rely on large-radix routers. Hamming graphs (Cartesian produc... more Current HPC and datacenter networks rely on large-radix routers. Hamming graphs (Cartesian products of complete graphs) and dragonflies (two-level direct networks with nodes organized in groups) are some direct topologies proposed for such networks. The original definition of the dragonfly topology is very loose, with several degrees of freedom such as the inter-and intra-group topology, the specific global connectivity and the number of parallel links between groups (or trunking level).
Proceedings of the 2013 Interconnection Network Architecture: On-Chip, Multi-Chip on - IMA-OCMC '13, 2013
ABSTRACT Dragonfly networks are composed of interconnected groups of routers. Adaptive routing al... more ABSTRACT Dragonfly networks are composed of interconnected groups of routers. Adaptive routing allows packets to be forwarded minimally or non-minimally adapting to the traffic conditions in the network. While minimal routing sends traffic directly between groups, non-minimal routing employs an intermediate group to balance network load. A random selection of this intermediate group (denoted as RRG) typically implies an extra local hop in the source group, what increases average path length and can reduce performance. In this paper we identify different policies for the selection of such intermediate group and explore their performance. Interestingly, simulation results show that an eager policy (denoted as CRG) that selects the intermediate group only between those directly connected to the ongoing router causes starvation in some network nodes. On the contrary, the best performance is obtained by a "mixed mode" policy (denoted as MM) that adds a local hop when the packet has moved away from the source router.
2008 IEEE International Symposium on Information Theory, 2008
Abstract In order to propose a new metric over QAM constellations, diagonal Gaussian graphs defin... more Abstract In order to propose a new metric over QAM constellations, diagonal Gaussian graphs defined over quotients of the Gaussian integers are introduced in this paper. Distance properties of the constellations are detailed by means of the vertex-to-vertex distribution of this family of graphs. Moreover, perfect codes for this metric are considered. Finally, notable subgraphs of diagonal Gaussian graphs are studied which leads to relate the proposed metric to other well-known graph-based metrics such as the Lee distance.
Advances in Mathematics of Communications, 2015
In this paper a wide family of identifying codes over regular Cayley graphs of degree four which ... more In this paper a wide family of identifying codes over regular Cayley graphs of degree four which are built over finite Abelian groups is presented. Some of the codes in this construction are also perfect. The graphs considered include some well-known graphs such as tori, twisted tori and Kronecker products of two cycles. Therefore, the codes can be used for identification in these graphs. Finally, an example of how these codes can be applied for adaptive identification over these graphs is presented.
IEEE Transactions on Parallel and Distributed Systems, 2015
Torus networks of moderate degree have been widely used in the supercomputer industry. Tori are s... more Torus networks of moderate degree have been widely used in the supercomputer industry. Tori are superb when used for executing applications that require near-neighbor communications. Nevertheless, they are not so good when dealing with global communications. Hence, typical 3D implementations have evolved to 5D networks, among other reasons, to reduce network distances. Most of these big systems are mixed-radix tori which are not the best option for minimizing distances and efficiently using network resources. This paper is focused on improving the topological properties of these networks.
The present work is devoted to characterize the family of symmetric undirected Cayley graphs over... more The present work is devoted to characterize the family of symmetric undirected Cayley graphs over finite Abelian groups for degrees 4 and 6. arXiv:1403.5440v1 [math.CO] From here onwards, all matrices will be considered to be non-singular, unless the contrary is stated. Note that, since Z n /M Z n has | det(M )| elements, this will be the number of nodes of Cay(Z n /M Z n ; ±B n ). Moreover, since any vertex v is adjacent to v ± e i (mod M ), Cay(Z n /M Z n ; ±B n ) is, in general, a regular graph of degree 2n, that is, any node has 2n different neighbours. Then, we call n the dimension of the graph. Note that when e i ≡ ±e j (mod M ) or 2e i ≡ 0 (mod M ) for some 1 ≤ i, j ≤ n then the degree of the Cayley graph is less than 2n. In that case we can also consider the corresponding multigraph, which always has degree 2n. The hypercube could be considered as an extreme case since ∀i ∈ {1, . . . , n}, 2e i ≡ 0 (mod M ) and therefore it has degree n.
A construction of 2-quasi-perfect Lee codes is given over the space Z n p for p prime, p ≡ ±5 (mo... more A construction of 2-quasi-perfect Lee codes is given over the space Z n p for p prime, p ≡ ±5 (mod 12) and n = 2[ p 4 ]. It is known that there are infinite such primes. Perfect codes for the Lee-metric were conjectured by Golomb and Welch not to exist, which has been proved for large radii and also for low dimension. The codes found are very close to be perfect, which tells about the nature of the conjecture. Some computations show that related graphs are Ramanujan, which could provide further connections between the fields.
The Journal of Supercomputing, 2014
2008 16th International Symposium on Field-Programmable Custom Computing Machines, 2008
Abstract The SMILE project attempts to build efficient lowcost clusters based on FPGA boards usin... more Abstract The SMILE project attempts to build efficient lowcost clusters based on FPGA boards using their reconfigurability capabilities. A real parallel application of Content-Based Information Retrieval over the SMILE cluster is presented. Using this application the SMILE cluster¿ s performance is evaluated and compared in terms of time and power consumption with traditional cluster architecture.
2012 IEEE 14th International Conference on High Performance Computing and Communication & 2012 IEEE 9th International Conference on Embedded Software and Systems, 2012
Abstract This paper analyzes the robustness of the king networks for fault tolerance. To this aim... more Abstract This paper analyzes the robustness of the king networks for fault tolerance. To this aim, a performance evaluation of two well known fault tolerant routing algorithms in king as well as 2d networks is done. Immunet that uses two virtual channels and Immucube, that has a better performance while requiring three virtual channels. Experimental results confirm the excellent behavior, both in performance and scalability, of the king topologies in the presence of failures. Finally, taking advantage of the topological features of king networks, ...
IEEE Transactions on Parallel and Distributed Systems, 2014
Torus networks of moderate degree have been widely used in the supercomputer industry. Tori are s... more Torus networks of moderate degree have been widely used in the supercomputer industry. Tori are superb when used for executing applications that require near-neighbor communications. Nevertheless, they are not so good when dealing with global communications. Hence, typical 3D implementations have evolved to 5D networks, among other reasons, to reduce network distances. Most of these big systems are mixed-radix tori, which are not the best option for minimizing distances and efficiently using network resources. This paper is focused on improving the topological properties of this kind of networks.
2008 International Conference on Field Programmable Logic and Applications, 2008
The SMILE project accelerates scientific and industrial applications by means of a cluster of low... more The SMILE project accelerates scientific and industrial applications by means of a cluster of low-cost FPGA boards. With this approach the intensive calculation tasks are accelerated using the FPGA logic, while the communication patterns of the applications remains unchanged by using a Message Passing Library over Linux. This paper explains the cluster architecture: the SMILE nodes and the developed high-speed