Core Graph Research Articles

Integrated core selection and mapping for mesh based Network-on-Chip design with irregular core sizes

Network-on-Chip (NoC) has been proposed to replace traditional bus based System-on-Chip (SoC) architecture to address the global communication challenges in nanoscale technologies. A major challenge in NoC based system design is to select Intellectual Property (IP) cores for implementing tasks and associate the selected cores to the routers to optimize cost and performance. These are commonly known as the process of core selection and application mapping respectively. In this paper, integrated core selection and mapping problem has been addressed. Mesh architecture has been considered for experimentation. The integrated core selection and mapping problem takes as input the application task graph, topology graph and a core library. It outputs the selected cores for the tasks and their mapping onto the topology graph, such that, all communication requirements of the application are satisfied. The cores present in a core library may perform more than one task and have non-uniform sizes. For this, a technique based on Particle Swarm Optimization (PSO) has been proposed to select cores from the given core library and map the resultant core graph onto mesh based architectures. An efficient heuristic for mapping has also been proposed, which maps the selected cores onto mesh based architectures, considering non-uniform core sizes. Comparisons have been carried out with step-by-step core selection and mapping approach and also with mapping algorithms that exist in the literature. Significant reductions have been observed in terms of communication cost over all the cases. Area comparisons have also been made. On average, improvement of 13.05% in communication cost and 2.07% in area have been observed. The proposed approach has also been compared in dynamic environment and significant reductions in the average network latency could be observed. On average, improvement of 5.48% in average network latency and 15.68% in network throughput has been observed. Comparison of energy consumption has also been done in both the cases.

Application Mapping onto Butterfly-Fat-Tree based Network-on-Chip using Discrete Particle Swarm Optimization

paper addresses the problem of application mapping onto Butterfly-Fat-Tree (BFT) based Network-on-Chip design. It proposes a new mapping technique based on discrete Particle Swarm Optimization (PSO) to map the cores of the core graph to the routers. The basic PSO has been augmented by running multiple PSO and deterministically generating a part of the initial population for PSO. The mapping results have been compared with well-known techniques reported in the literature for a number of benchmark applications. The reported strategy produces results superior to those obtained via existing approaches within a reasonable CPU time. Keywordsmapping, Network-on-Chip, System-on-Chip, Butterfly-Fat-Tree, Discrete Particle Swarm Optimization

Fast graph mining with HBase

Mining large graphs using distributed platforms has attracted a lot of research interests. Especially, large graph mining on Hadoop has been researched extensively, due to its simplicity and massive scalability. However, the design principle of Hadoop to maximize scalability often limits the efficiency of the graph algorithms. For this reason, the performance of graph mining algorithms running on top of Hadoop has not been satisfactory.In this paper, we propose Unicorn, a graph mining library on top of HBase, an open source version of Bigtable. Unicorn exploits the random write characteristic of HBase to improve the performance of generalized iterative matrix–vector multiplication (GIM–V), a core graph mining routine. Extensive experiments show that Unicorn outperforms its predecessors by an order of magnitude for a graph with 68 billion edges.

Thermal Uniformity-Aware Application Mapping for Network-on-Chip Design

thermal-uniformity in an integrated circuit chip is very essential for its correct operation. Thus, in the Network- on-Chip (NoC) based system design as well, it is essential to attach cores of the application core graph to the routers in the topology graph so that thermal uniformity across the chip is maintained. However, the performance of the application should not be sacrificed to a great extent. Also, the CPU time needed to explore the overall search-space is quite high. This paper presents a tool to the designers to explore the search- space in a controlled fashion. The designer can specify the communication cost degradation that can be tolerated and the amount of effort put in to identify the potential solutions. All non-dominated solutions (in terms of communication cost and temperature variance) are reported from which the designer can choose the appropriate one for implementation.

Efficient and Dynamic Algorithms for Alternating Büchi Games and Maximal End-Component Decomposition

The computation of the winning set for Büchi objectives in alternating games on graphs is a central problem in computer-aided verification with a large number of applications. The long-standing best known upper bound for solving the problem is Õ ( n · m ), where n is the number of vertices and m is the number of edges in the graph. We are the first to break the Õ ( n · m ) boundary by presenting a new technique that reduces the running time to O ( n 2 ). This bound also leads to O ( n 2 )-time algorithms for computing the set of almost-sure winning vertices for Büchi objectives (1) in alternating games with probabilistic transitions (improving an earlier bound of Õ ( n · m )), (2) in concurrent graph games with constant actions (improving an earlier bound of O ( n 3 )), and (3) in Markov decision processes (improving for m > n 4/3 an earlier bound of O ( m · √ m )). We then show how to maintain the winning set for Büchi objectives in alternating games under a sequence of edge insertions or a sequence of edge deletions in O ( n ) amortized time per operation. Our algorithms are the first dynamic algorithms for this problem. We then consider another core graph theoretic problem in verification of probabilistic systems, namely computing the maximal end-component decomposition of a graph. We present two improved static algorithms for the maximal end-component decomposition problem. Our first algorithm is an O ( m · √ m )-time algorithm, and our second algorithm is an O ( n 2 )-time algorithm which is obtained using the same technique as for alternating Büchi games. Thus, we obtain an O (min {m · √ m , n 2 })-time algorithm improving the long-standing O ( n · m ) time bound. Finally, we show how to maintain the maximal end-component decomposition of a graph under a sequence of edge insertions or a sequence of edge deletions in O ( n ) amortized time per edge deletion, and O ( m ) worst-case time per edge insertion. Again, our algorithms are the first dynamic algorithms for this problem.

Telemaco: A Language Oriented Tool for Graph-based Models Layout Optimization

Progress of ICT is shifting the paradigm of systems organization towards a distributed approach, in which physical deployment of components influences the evaluation of systems properties. This contribution can be considered as a problem of graph layout optimization, well-known in literature where several approaches have been exploited in different application fields with different solving techniques. Then again, complex systems can be only studied by means of different formalisms which codification is the aim of language engineering. Telemaco is a tool that supports a novel approach for the application of graph layout optimizations to heterogeneous models, based on the OsMoSys framework and on the language engineering principles. It can cope with different graph-based formalisms by exploiting either their core graph nature or their different specialized features by means of language hierarchies. In this paper Telemaco is introduced together with its foundations and an example of application to Wireless Sensor Networks (WSN) deployment.

A fault‐tolerant core mapping technique in networks‐on‐chip

This study proposes a fault-tolerant technique on application mapping and spare core allocation in networks-on-chip. The proposed technique sets the place of spare cores among free non-faulty processing cores, dynamically. Here, dynamically setting means that the places of spare cores are tuned for each application and are not fixed in the platform statically. Some vertices of each application core graph can be known as critical, based on their vulnerabilities, the performance degradation and the energy consumption overheads because of negative impacts of failure recovery. This technique locates the spare cores near to the critical cores. As the main theoretical contribution, the problem of spare core placement and its impression on system fault-tolerance properties is discussed. Some metrics are investigated to be considered in spare core allocation. The results of 1 000 000 fault injection experiments show that the proposed technique leads to communication energy reductions and performance improvement, compared with related works.

Detecting protein complexes based on relevancy from protein interaction networks

In protein-protein interaction networks, proteins combine into macromolecular complexes to execute essential functions in the cells, such as replication, transcription, protein transport. To solve the problem of detecting protein complexes from protein interaction networks, we used relevant graph and irrelevant graph to represent the relation of connection between a node and a core graph. We defined a variable Relevancy to represent whether a node had a dense or loose connection to a core graph. Then we proposed the Relevancy Judgment algorithm to detecting protein complexes from protein interaction networks. Our algorithm decided whether a node belonged to a protein complex through judging the relevancy between core graph and nodes out of core graph. Experiment results show that our algorithm has an excellent performance in both accuracy and hit rate.

Distributed socialite

Large-scale graph analysis is becoming important with the rise of world-wide social network services. Recently in SociaLite, we proposed extensions to Datalog to efficiently and succinctly implement graph analysis programs on sequential machines. This paper describes novel extensions and optimizations of SociaLite for parallel and distributed executions to support large-scale graph analysis.With distributed SociaLite, programmers simply annotate how data are to be distributed, then the necessary communication is automatically inferred to generate parallel code for cluster of multi-core machines. It optimizes the evaluation of recursive monotone aggregate functions using a delta stepping technique. In addition, approximate computation is supported in SociaLite, allowing programmers to trade off accuracy for less time and space.We evaluated SociaLite with six core graph algorithms used in many social network analyses. Our experiment with 64 Amazon EC2 8-core instances shows that SociaLite programs performed within a factor of two with respect to ideal weak scaling. Compared to optimized Giraph, an open-source alternative of Pregel, SociaLite programs are 4 to 12 times faster across benchmark algorithms, and 22 times more succinct on average.As a declarative query language, SociaLite, with the help of a compiler that generates efficient parallel and approximate code, can be used easily to create many social apps that operate on large-scale distributed graphs.

Detecting Protein Complexes through Micro-Network Comparison in Protein-Protein Interaction Networks

Proteins are likely to form closely coupled protein complexes as functional units to participate in biological processes. We propose a Micro-Network Comparison algorithm to solve the problem of detecting protein complexes from protein interaction networks. We express the characters of a connection between a node and a core graph through the In-module Micro-network graph and Out-module Micro-network graph. We compare the number of edges in two graphs to decide whether a node has a dense or loose connection to a core graph. We give four experimental results using the algorithm and the results show that our algorithm has an excellent performance in both accuracy and hit rate.

Constrained De Novo Sequencing of Conotoxins

De novo peptide sequencing by mass spectrometry (MS) can determine the amino acid sequence of an unknown peptide without reference to a protein database. MS-based de novo sequencing assumes special importance in focused studies of families of biologically active peptides and proteins, such as hormones, toxins, and antibodies, for which amino acid sequences may be difficult to obtain through genomic methods. These protein families often exhibit sequence homology or characteristic amino acid content; yet, current de novo sequencing approaches do not take advantage of this prior knowledge and, hence, search an unnecessarily large space of possible sequences. Here, we describe an algorithm for de novo sequencing that incorporates sequence constraints into the core graph algorithm and thereby reduces the search space by many orders of magnitude. We demonstrate our algorithm in a study of cysteine-rich toxins from two cone snail species (Conus textile and Conus stercusmuscarum) and report 13 de novo and about 60 total toxins.

A3MAP

In this article, we propose novel and global Architecture-Aware Analytic MAPping (A3MAP) algorithms applied to Networks-on-Chip (NoCs) not only with homogeneous Processing Elements (PEs) on a regular mesh network as done by most previous application mapping algorithms but also with heterogeneous PEs on an irregular mesh or custom network. As the main contributions, we develop a simple yet efficient interconnection matrix that can easily model any core graph and network. Then, an application mapping problem is exactly formulated to Mixed Integer Quadratic Programming (MIQP). Since MIQP is NP-hard, we propose two effective heuristics, a successive relaxation algorithm achieving short runtime, called A3MAP-SR and a genetic algorithm achieving high mapping quality, called A3MAP-GA. We also propose a partition-based application mapping approach for large-scale NoCs, which provides better trade-off between performance and runtime. Experimental results show that A3MAP algorithms reduce total hop count, compared to the previous application mapping algorithms optimized for a regular mesh network, called NMAP [Murali and Micheli 2004] and for an irregular mesh and custom network, called CMAP [Tornero et al. 2008]. Furthermore, A3MAP algorithms make packets travel shorter distance than CMAP, which is related to energy consumption.

Finite dualities and map-critical graphs on a fixed surface

Let K be a class of graphs. A pair ( F , U ) is a finite duality in K if U ∈ K , F is a finite set of graphs, and for any graph G in K we have G ⩽ U if and only if F ⩽̸ G for all F ∈ F , where “⩽” is the homomorphism order. We also say U is a dual graph in K . We prove that the class of planar graphs has no finite dualities except for two trivial cases. We also prove that the class of toroidal graphs has no 5-colorable dual graphs except for two trivial cases. In a sharp contrast, for a higher genus orientable surface S we show that Thomassenʼs result (Thomassen, 1997 [17]) implies that the class, G ( S ) , of all graphs embeddable in S has a number of finite dualities. Equivalently, our first result shows that for every planar core graph H except K 1 and K 4 , there are infinitely many minimal planar obstructions for H-coloring (Hell and Nešetřil, 1990 [4]), whereas our later result gives a converse of Thomassenʼs theorem (Thomassen, 1997 [17]) for 5-colorable graphs on the torus.

CIRCUITS IN GRAPHS THROUGH A PRESCRIBED SET OF ORDERED VERTICES

A circuit in a simple undirected graph G = (V, E) is a sequence of vertices {v1, v2, …, vk+1} such that v1 = vk+1 and {vi, vi+1} ∈ E for i = 1, …, k. A circuit C is said to be edge-simple if no edge of G is used twice in C. In this article we study the following problem: which is the largest integer k such that, given any subset of k ordered vertices of a graph G, there exists an edge-simple circuit visiting the k vertices in the prescribed order? We first study the case when G has maximum degree at most 3, establishing the value of k for several subcases, such as when G is planar or 3-vertex-connected. Our main result is that k = 10 in infinite square grids. To prove this, we introduce a methodology based on the notion of core graph, in order to reduce the number of possible vertex configurations, and then we test each one of the resulting configurations with an Integer Linear Program (ILP) solver.

Vessel tracking by connecting the dots

We propose an algorithm for tracking blood vessel segments in Computed Tomographic (CT) images. Our procedure first finds core points that tend to concentrate along the centerlines of vessels. Intuitively, the core points are centers of intensity plateaus in two-dimensional slices through the input image. The starting and the end point of the desired vessel (S and E) are also considered core points. The weighted core graph is built by connecting nearby core points with edges. Edge weights are designed so that edges of large weights are unlikely to follow a vessel segment. We compute the shortest path connecting S and E in the core graph. The output is the result of applying shortcutting operations to this path.

Non-planar core reduction of graphs

We present a reduction method that reduces a graph to a smaller core graph which behaves invariant with respect to non-planarity measures like crossing number, skewness, coarseness, and thickness. The core reduction is based on the decomposition of a graph into its triconnected components and can be computed in linear time. It has applications in heuristic and exact optimization algorithms for the non-planarity measures mentioned above. Experimental results show that this strategy reduces the number of edges by 45% in average for a widely used benchmark set of graphs.

The circuit polynomial of the restricted rooted product [formula omitted] of graphs with a bipartite core G

As an instance of the B-polynomial, the circuit, or cycle, polynomial P ( G ( Γ ) ; w ) of the generalized rooted product G ( Γ ) of graphs was studied by Farrell and Rosenfeld [Block and articulation node polynomials of the generalized rooted product of graphs, J. of Math. Sci. (India) 11(1) (2000) 35–47] and Rosenfeld and Diudea [The block polynomials and block spectra of dendrimers, Internet Electron. J. Mol. Design 1(3) (2002) 142–156]. In both cases, the rooted product G ( Γ ) was considered without any restrictions on graphs G and Γ . Herein, we present a new general result and its corollaries concerning the case when the core graph G is restricted to be bipartite.

On nut and core singular fullerenes

A graph G is singular of nullity η ( > 0 ) , if its adjacency matrix A is singular, with the eigenvalue zero of multiplicity η . A singular graph having a 0-eigenvector, x , with no zero entries, is called a core graph. We place particular emphasis on nut graphs, namely the core graphs of nullity one. Through symmetry considerations of the automorphism group of the graph, we study relations among the entries of x which lead to interesting implications in chemistry. The zero eigenvalue is rare in a fullerene graph. We show that there are possible nut fullerenes with relatively simple structures.

Hierarchical management protocol for constructing a QoS communication path in wireless Ad Hoc networks

An Ad Hoc network consists of mobile hosts that can dynamically construct a wireless network without base stations. Due to the limited communication range, a source host usually needs other hosts to relay messages to the destination in a multi-hop manner. Consequently, establishing a routing path from the source to the destination is a basic requirement for providing communication service between any pair of mobile hosts. This study proposes a two-level management approach for efficiently constructing and maintaining a QoS routing path in Ad Hoc wireless networks, significantly reducing the quantity of control packets. In the first phase, the mobile hosts are partitioned into a number of complete graphs, each represented by a Supernode managed by an agent. The Ad Hoc network topology is thus transformed to an Agent-based Graph ( AG). In the second phase, some agents of a larger degree than neighboring agents are selected as core nodes. The core nodes then virtually construct a Core Graph ( CG). The proposed two-level hierarchical management and bandwidth-looking-ahead technologies can efficiently establish and maintain a QoS communication path at a low control packet cost. Simulation results indicate that the proposed management model significantly reduces the number of control packets in areas with very large numbers of mobile hosts.

Short Answers to Exponentially Long Questions: Extremal Aspects of Homomorphism Duality

We prove that there exists a constant k such that for every $n \geq 1$ there exists a directed core graph $H_n$ with at least $2^n$ vertices such that a directed graph G is $H_n$-colorable if and only if every subgraph of G with at most $kn\log(n)$ vertices is $H_n$-colorable. Our examples show that in general the "duals of relational structures" in the sense of [J. Nesetril and C. Tardif, J. Combin. Theory Ser. B, 80 (2000), pp. 80-97] can have superpolynomial size. The construction given in this paper gives a double exponential upper bound for such a construction. Here we improve this to an exponential upper bound.