Esteban Stafford | Universidad de Cantabria (original) (raw)
Papers by Esteban Stafford
IEEE Transactions on Parallel and Distributed Systems, 2015
In the late years many different interconnection networks have been used with two main tendencies... 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.
Future Generation Computer Systems
The Journal of Supercomputing
The Journal of Supercomputing, 2016
Proceedings of the 16th International Euro Par Conference on Parallel Processing Part Ii, 2010
Proceedings of the 16th International Euro Par Conference on Parallel Processing Part Ii, 2010
16th IEEE International Conference on High Performance Computing and Communications (HPCC 2014). Paris (France), 2014
King networks were proposed as higher degree alternatives to 2D tori and meshes. These networks o... more King networks were proposed as higher degree alternatives to 2D tori and meshes. These networks offer improved throughput and latency with minimum distance routing in benign traffic patterns. As a solution to performance problems in adverse traffic pattern of the minimal routing, this article presents a missrouting solution. It uses two parameters to control the generation of routing tables. Using the paths on these tables, packets reach their destination nodes through non-minimal paths, without deadlock, livelock or starvation. Optimal values for the parameters are empirically determined. This routing strategy slightly improves the throughput while hardly increasing the base latency and extending the linear behaviour of the network. Experimental results confirm the good properties of this algorithm compared to minimal routing and Valiant algorithms.
—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.
In this paper we propose two new topologies for on-chip networks that we have denoted as king mes... more In this paper we propose two new topologies for on-chip networks 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 and diagonal movements like the king on a chess board. First we present a topological study addressing distance properties, bisection bandwidth and path diversity as well as a folding scheme. Second we analyze different routing mechanisms. Ranging from minimal distance routings to missrouting techniques which exploit the topological richness of these networks. Finally we make an exhaustive performance evaluation comparing the new king topologies with their classical counterparts. The experimental results show a performance improvement, that allow us to present these new topologies as better alternative to classical topologies.
2013 Euromicro Conference on Digital System Design, 2013
ABSTRACT Many current VLSI on-chip multiprocessors and systems-on-chip employ point-to-point swit... more ABSTRACT Many current VLSI on-chip multiprocessors and systems-on-chip employ point-to-point switched interconnection networks. Rings and 2D-meshes are among the most popular interconnection topologies for these increasingly important onchip networks. Nevertheless, rings cannot scale beyond dozens of nodes and meshes are asymmetric. Two of the key features of square 2D-tori are their scalability and symmetry. As higher scalability is demanded by the increasing number of cores (or specialized units) integrated on a chip and symmetry is critical for high-performance and load balancing, we concentrate on 2D-tori. However, most popular deadlock-free routing mechanisms are based on Dimension Order Routing (DOR) which breaks the torus symmetry when managing adversarial traffic patterns. This paper analyzes this problem and its consequences. After that, it proposes a new deadlock-free fully adaptive minimal routing, denoted as σDOR, that preserves tori symmetry under any load. It uses just two virtual channels to avoid DOR-induced asymmetry, the same as in previous competitive proposals. σDOR exhibits better behavior than any of previous solutions as it allows packets to dynamically adapt to local congestion. Experimental results evidence the superior performance of our mechanism, confirming the negative impact of DOR asymmetry.
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, 2015
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.
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 ...
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.
Euro-Par 2010-Parallel …, Jan 1, 2010
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, ...
2007 IEEE International Symposium on Information Theory, 2007
... the code defined as the left ideal generated by this element is a perfect 1-error correcting ... more ... the code defined as the left ideal generated by this element is a perfect 1-error correcting code for the Lipschitz graph distance over H(7L)>. In general, this set is four dimensional, but next we study some cases in which this lattice can berepresented as a two-dimensional one. ...
IEEE Transactions on Parallel and Distributed Systems, 2015
In the late years many different interconnection networks have been used with two main tendencies... 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.
Future Generation Computer Systems
The Journal of Supercomputing
The Journal of Supercomputing, 2016
Proceedings of the 16th International Euro Par Conference on Parallel Processing Part Ii, 2010
Proceedings of the 16th International Euro Par Conference on Parallel Processing Part Ii, 2010
16th IEEE International Conference on High Performance Computing and Communications (HPCC 2014). Paris (France), 2014
King networks were proposed as higher degree alternatives to 2D tori and meshes. These networks o... more King networks were proposed as higher degree alternatives to 2D tori and meshes. These networks offer improved throughput and latency with minimum distance routing in benign traffic patterns. As a solution to performance problems in adverse traffic pattern of the minimal routing, this article presents a missrouting solution. It uses two parameters to control the generation of routing tables. Using the paths on these tables, packets reach their destination nodes through non-minimal paths, without deadlock, livelock or starvation. Optimal values for the parameters are empirically determined. This routing strategy slightly improves the throughput while hardly increasing the base latency and extending the linear behaviour of the network. Experimental results confirm the good properties of this algorithm compared to minimal routing and Valiant algorithms.
—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.
In this paper we propose two new topologies for on-chip networks that we have denoted as king mes... more In this paper we propose two new topologies for on-chip networks 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 and diagonal movements like the king on a chess board. First we present a topological study addressing distance properties, bisection bandwidth and path diversity as well as a folding scheme. Second we analyze different routing mechanisms. Ranging from minimal distance routings to missrouting techniques which exploit the topological richness of these networks. Finally we make an exhaustive performance evaluation comparing the new king topologies with their classical counterparts. The experimental results show a performance improvement, that allow us to present these new topologies as better alternative to classical topologies.
2013 Euromicro Conference on Digital System Design, 2013
ABSTRACT Many current VLSI on-chip multiprocessors and systems-on-chip employ point-to-point swit... more ABSTRACT Many current VLSI on-chip multiprocessors and systems-on-chip employ point-to-point switched interconnection networks. Rings and 2D-meshes are among the most popular interconnection topologies for these increasingly important onchip networks. Nevertheless, rings cannot scale beyond dozens of nodes and meshes are asymmetric. Two of the key features of square 2D-tori are their scalability and symmetry. As higher scalability is demanded by the increasing number of cores (or specialized units) integrated on a chip and symmetry is critical for high-performance and load balancing, we concentrate on 2D-tori. However, most popular deadlock-free routing mechanisms are based on Dimension Order Routing (DOR) which breaks the torus symmetry when managing adversarial traffic patterns. This paper analyzes this problem and its consequences. After that, it proposes a new deadlock-free fully adaptive minimal routing, denoted as σDOR, that preserves tori symmetry under any load. It uses just two virtual channels to avoid DOR-induced asymmetry, the same as in previous competitive proposals. σDOR exhibits better behavior than any of previous solutions as it allows packets to dynamically adapt to local congestion. Experimental results evidence the superior performance of our mechanism, confirming the negative impact of DOR asymmetry.
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, 2015
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.
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 ...
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.
Euro-Par 2010-Parallel …, Jan 1, 2010
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, ...
2007 IEEE International Symposium on Information Theory, 2007
... the code defined as the left ideal generated by this element is a perfect 1-error correcting ... more ... the code defined as the left ideal generated by this element is a perfect 1-error correcting code for the Lipschitz graph distance over H(7L)>. In general, this set is four dimensional, but next we study some cases in which this lattice can berepresented as a two-dimensional one. ...