The modern integrated circuit is one of the most complex products that has been engineered to-date. It continues to grow in complexity as the years progress. As a result, very large-scale integrated (VLSI) circuit design now involves massive design teams employing state-of-the art computer-aided design (CAD) tools. One of the oldest, yet most important CAD problems for VLSI circuits is physical design automation, where one needs to compute the best physical layout of millions to billions of circuit components on a tiny silicon surface Lim08 . The process of mapping an electronic design to a chip involves a number of physical design stages, one of which is clustering. In this paper, we focus on problems in clustering which are critical for more sustainable chips. The clustering problem in combinatorial circuits alone is a source of multiple models. In particular, we consider the problem of clustering combinatorial circuits for delay minimization, when logic replication is not allowed ( CN ). The problem of delay minimization when logic replication is allowed ( CA ) has been well studied, and is known to be solvable in polynomial-time Wong1 . However, unbounded logic replication can be quite expensive. Thus, CN is an important problem. We show that selected variants of CN are NP-hard . We also obtain approximability and inapproximability results for these problems. A preliminary version of this paper appeared in Don15 .
In @cite_8 a polynomial-time optimal solution to the clustering problem is given assuming the unit delay model. In this model, there is no delay that is associated with any gate or with any edge linking two gates within a cluster. A delay of one unit of time is assumed along any edge crossing a cluster boundary. Let us note that in that paper replication of the logic is allowed, that is, a node may be present in many clusters. The more general delay model considered in this paper is presented in @cite_5 . In that paper an algorithm is given that constructs a clustering that aims to minimize the delay under the general delay model. Let us note that the algorithm achieves optimum delay under some specific conditions. In @cite_2 another clustering algorithm is presented, and in the same paper it is proved that the algorithm always finds the optimum clustering.
@cite_5 @cite_2 @cite_8
2157661053 1988118342 1982882434
An important aspect of the packaging of digital networks is the allocation of logic gates to modules such that a predetermined objective function is minimized. In order to develop techniques for this partitioning of a logic network we have considered the following problem: Given an acyclic combinational network composed of various primitive blocks such as NOR gates, assume that a maximum of M gates can be "clustered" together into larger modules, and that a maximum of P pins can be accommodated in each larger module. Assume also that in a network composed of such larger modules, no delay is encountered on the interconnections linking two gates internal to a module and a delay of one time unit is encountered on interconnections linking two gates in different modules . Find an easily applied algorithm that will result in a network such that the maximum delay through the network is minimized. The authors address the problem of clustering a circuit for minimizing its delay, subject to capacity constraints on the clusters. They present an algorithm for combinational circuits and give sufficient conditions under which it is optimum. In addition, they address the problem of minimizing the number of clusters and nodes without increasing the maximum delay found by the algorithm. Finally, they extend the clustering algorithm to minimize the clock cycle of a sequential synchronous circuit. > This paper addresses the problem of circuit clustering for delay minimization, subject to capacity constraints. We use the general delay model, for which only heuristic solutions were known. We present an optimal polynomial time algorithm for combinational circuits under this model. Our algorithm can be generalized to solve the problem under any monotone clustering constraint. Remote clouds are gradually unable to achieve ultra-low latency to meet the requirements of mobile users because of the intolerable long distance between remote clouds and mobile users and the network congestion caused by the tremendous number of users. Mobile edge computing, a new paradigm, has been proposed to mitigate aforementioned effects. Existing studies mostly assume the edge servers have been deployed properly and they just pay attention to how to minimize the delay between edge servers and mobile users. In this paper, considering the practical environment, we investigate how to deploy edge servers effectively and economically in wireless metropolitan area networks. Thus, we address the problem of minimizing the number of edge servers while ensuring some QoS requirements. Aiming at more consistence with a generalized condition, we extend the definition of the dominating set, and transform the addressed problem into the minimum dominating set problem in graph theory. In addition, two conditions are considered for the capacities of edge servers: one is that the capacities of edge servers can be configured on demand, and the other is that all the edge servers have the same capacities. For the on-demand condition, a greedy based algorithm is proposed to find the solution, and the key idea is to iteratively choose nodes that can connect as many other nodes as possible under the delay, degree and cluster size constraints. Furthermore, a simulated annealing based approach is given for global optimization. For the second condition, a greedy based algorithm is also proposed to satisfy the capacity constraint of edge servers and minimize the number of edge servers simultaneously. The simulation results show that the proposed algorithms are feasible. Sequential time series clustering is a technique used to extract important features from time series data. The method can be shown to be the process of clustering in the delay-vector space formalism used in the Dynamical Systems literature. Recently, the startling claim was made that sequential time series clustering is meaningless. This has important consequences for a significant amount of work in the literature, since such a claim invalidates these work’s contribution. In this paper, we show that sequential time series clustering is not meaningless, and that the problem highlighted in these works stem from their use of the Euclidean distance metric as the distance measure in the delay-vector space. As a solution, we consider quite a general class of time series, and propose a regime based on two types of similarity that can exist between delay vectors, giving rise naturally to an alternative distance measure to Euclidean distance in the delay-vector space. We show that, using this alternative distance measure, sequential time series clustering can indeed be meaningful. We repeat a key experiment in the work on which the “meaningless” claim was based, and show that our method leads to a successful clustering outcome. We study a mobile wireless network where groups or clusters of nodes are intermittently connected via mobile carriers'' (the carriers provide connectivity over time among different clusters of nodes). Over such networks (an instantiation of a delay tolerant network), it is well-known that traditional routing algorithms perform very poorly. In this paper, we propose a two-level Back- Pressure with Source-Routing algorithm (BP+SR) for such networks. The proposed BP+SR algorithm separates routing and scheduling within clusters (fast time-scale) from the communications that occur across clusters (slow time-scale), without loss in network throughput (i.e., BP+SR is throughput-optimal). More importantly, for a source and destination node that lie in different clusters, the traditional back-pressure algorithm results in large queue lengths at each node along its path. This is because the queue dynamics are driven by the slowest time-scale (i.e., that of the carrier nodes) along the path between the source and destination, which results in very large end-to-end delays. On the other-hand, we show that the two-level BP+SR algorithm maintains large queues only at a very few nodes, and thus results in order-wise smaller end-to-end delays. We provide analytical as well as simulation results to confirm our claims. We consider the Correlation Clustering problem introduced in [2]. Given a graph G = (V,E) where each edge is labeled either "+" (similar) or "-" (different), we want to cluster the nodes so that the + edges lie within the clusters and the -- edges lie between clusters. Specifically, we want to maximize agreements --- the number of + edges within clusters and -- edges between clusters. This problem is NP-Hard [2]. We give a 0.7666-approximation algorithm for maximizing agreements on any graph even when the edges have non-negative weights (along with labels) and we want to maximize the weight of agreements. These were posed as open problems in [2]. Previously the only results known were a trivial 0.5-approximation for arbitrary edge weighted graphs, and a PTAS with unit edge weights when |E| = Ω(|V|2). Somewhat surprisingly, our algorithm always produces a clustering with at most 6 clusters. As a corollary we get a 0.7666-approximation algorithm for the k-clustering variant of the problem where we may create at most k clusters. A major component of this algorithm is a simple, easy-to-analyze algorithm that by itself achieves an approximation ratio of 0.75, opening at most 4 clusters. One of the most compelling technological advances of this decade has been the advent of deploying wireless networks of heterogeneous smart sensor nodes for complex information gathering tasks. A wireless distributed sensor network (DSN) is a self-organizing , ad-hoc network of a large number of cooperative intelligent sensor nodes. Due to the limited power of sensor nodes, energy-efficient DSN are essentially multi-hop networks. The self-organizing capabilities, and the cooperative operation of DSN allow for forming reliable clusters of sensors deployed near, or at, the sites of target phenomena. Reliable monitoring of a phenomenon (or event detection) depends on the collective data provided by the target cluster of sensors, and not on any individual node. The failure of one or more nodes may not cause the operational data sources to be disconnected from the data sinks (command nodes or end user stations). However, it may increase the number of hops a data message has to go through before reaching its destination (and subsequently increase the message delay). In this paper, we focus on two related problems: computing a measure for the reliability of DSN, and computing a measure for the expected & the maximum message delay between data sources (sensors) & data sinks in an operational DSN. Given an estimation of the failure probabilities of the sensors, as well as the intermediate nodes (nodes used to relay messages between data sources, and data sinks), we use a probabilistic graph to model DSN. We define the DSN reliability as the probability that there exists an operating communication path between the sink node, and at least one operational sensor in a target cluster. We show that both problems are #P-hard for arbitrary networks. We then present two algorithms for computing the reliability, and the expected message delay for arbitrary networks. We also consider two special cases where efficient (polynomial time) algorithms are developed. Finally, we present some numerical results that demonstrate some of the applications of our algorithms. In this paper we investigate the connectivity for large-scale clustered wireless sensor and ad hoc networks. We study the effect of mobility on the critical transmission range for asymptotic connectivity in k-hop clustered networks, and compare to existing results on non-clustered stationary networks. By introducing k-hop clustering, any packet from a cluster member can reach a cluster head within k hops, and thus the transmission delay is bounded as Θ(1) for any finite k. We first characterize the critical transmission range for connectivity in mobile k-hop clustered networks where all nodes move under either the random walk mobility model with non-trivial velocity or the i.i.d. mobility model. By the term non-trivial velocity, we mean that the velocity of nodes v is Θ(1). We then compare with the critical transmission range for stationary k-hop clustered networks. We also study the transmission power versus delay trade-off and the average energy consumption per flow among different types of networks. We show that random walk mobility with non-trivial velocity increases connectivity in k-hop clustered networks, and thus significantly decreases the energy consumption and improves the power-delay trade-off. The decrease of energy consumption per flow is shown to be Θ(logn nd ) in clustered networks. These results provide insights on network design and fundamental guidelines on building a large-scale wireless network. In this paper, we investigate the connectivity for large-scale clustered wireless sensor and ad hoc networks. We study the effect of mobility on the critical transmission range for asymptotic connectivity in k-hop clustered networks and compare to existing results on nonclustered stationary networks. By introducing k -hop clustering, any packet from a cluster member can reach a cluster head within k hops, and thus the transmission delay is bounded as Θ(1) for any finite k. We first characterize the critical transmission range for connectivity in mobile k-hop clustered networks where all nodes move under either the random walk mobility model with nontrivial velocity or the i.i.d. mobility model. By the term nontrivial velocity, we mean that the velocity of a node v is ω(r(n)), where r(n) is the transmission range of the node. We then compare with the critical transmission range for stationary k-hop clustered networks. In addition, the critical number of neighbors is studied in a parallel manner for both stationary and mobile networks. We also study the transmission power versus delay tradeoff and the average energy consumption per flow among different types of networks. We show that random walk mobility with nontrivial velocities increases connectivity in k-hop clustered networks, and thus significantly decreases the energy consumption and improves the power-delay tradeoff. The decrease of energy consumption per flow is shown to be Θ([(logn) (nd)]) in clustered networks. These results provide insights on network design and fundamental guidelines on building a large-scale wireless network. This paper investigates the optimal rate allocation problem with end-to-end delay constraints in multi-hop wireless networks. We introduce Virtual Link Capacity Margin (VLCM), which is the gap between the schedulable link capacity and the maximum allowable flow rate over a link, for link delay control. We formulate the problem as a utility maximization framework with two sets of constraints: 1) capacity and schedulability constraints and 2) end-to-end delay constraints. By dual decomposition of the original optimization problem, we present a control algorithm that jointly tunes the flow rates and VLCMs, through a double-price scheme derived with regard to the constraints: the link congestion price reflecting the traffic load of a link, and the flow delay price reflecting the margin between the average packet delay and the delay requirement of a flow. We prove that the algorithm converges to a global optimum where the aggregate network utility defined over the flow rate set is maximized, while the delay constraints are satisfied. A key feature of our algorithm is it does not rely on a specific traffic model. The algorithm is implemented distributedly via joint wireless link scheduling and congestion control. Simulation results show that our algorithm outperforms heuristic rate allocation algorithms while satisfying the end-to-end delay constraints. In this paper we present an algorithm for recognizing walking pedestrians in sequences of color images taken from a moving camera. The recognition is based on the characteristic motion of the legs of a pedestrian walking parallel to the image plane. Each image is segmented into region-like image parts by clustering pixels in a combined color position feature space. The proposed clustering technique implies matching of corresponding clusters in consecutive frames and therefore allows clusters to be tracked over a sequence of images. Based on the observation of clusters over time a two-stage classifier extracts those clusters which most likely represent the legs of pedestrians. A fast polynomial classifier performs a rough preselection of clusters by evaluating temporal changes of a shape-dependent clusters feature. The final classification is done by a time delay neural network (TDNN) with spatio-temporal receptive fields. In packet audio applications, packets are buffered at a receiving site and their playout delayed in order to com- pensate for variable network delays. In this paper, we con- sider the problem of adaptively adjusting the playout delay in order to keep this delay as small as possible, while at the same time avoiding excessive "loss" due to the arrival of packets at the receiver after their playout time has al- ready passed. The contributions of this paper are twofold. First, given a trace of packet audio receptions at a receiver, we present efficient algorithms for computing a bound on the achievable performance of any playout delay adjustment algorithm. More precisely, we compute upper and lower bounds (which are shown to be tight for the range of loss and delay values of interest) on the optimum (minimum) average playout delay for a given number of packet losses (due to late arrivals) at the receiver for that trace. Second, we present a new adaptive delay adjustment algorithm that tracks the network delay of recently received packets and efficiently maintains delay percentile information. This in- formation, together with a "delay spike" detection algorithm based on (but extending) our earlier work, is used to dy- namically adjust talkspurt playout delay. We show that this algorithm outperforms existing delay adjustment algorithms over a number of measured audio delay traces and performs close to the theoretical optimum over a range of parameter values of interest. This paper investigates the use of instantly decodable network coding (IDNC) for minimizing the mean decoding delay in multicast cooperative data exchange systems, where the clients cooperate with each other to obtain their missing packets. Here, IDNC is used to reduce the decoding delay of each transmission across all clients. We first introduce a new framework to find the optimum client and coded packet that result in the minimum mean decoding delay. However, since finding the optimum solution of the proposed framework is NP-hard, we further propose a heuristic algorithm that aims to minimize the lower bound on the expected decoding delay in each transmission. The effectiveness of the proposed algorithm is assessed through simulations. This paper introduces McPAT, an integrated power, area, and timing modeling framework that supports comprehensive design space exploration for multicore and manycore processor configurations ranging from 90nm to 22nm and beyond. At the microarchitectural level, McPAT includes models for the fundamental components of a chip multiprocessor, including in-order and out-of-order processor cores, networks-on-chip, shared caches, integrated memory controllers, and multiple-domain clocking. At the circuit and technology levels, McPAT supports critical-path timing modeling, area modeling, and dynamic, short-circuit, and leakage power modeling for each of the device types forecast in the ITRS roadmap including bulk CMOS, SOI, and doublegate transistors. McPAT has a flexible XML interface to facilitate its use with many performance simulators. Combined with a performance simulator, McPAT enables architects to consistently quantify the cost of new ideas and assess tradeoffs of different architectures using new metrics like energy-delay-area2 product (EDA2P) and energy-delay-area product (EDAP). This paper explores the interconnect options of future manycore processors by varying the degree of clustering over generations of process technologies. Clustering will bring interesting tradeoffs between area and performance because the interconnects needed to group cores into clusters incur area overhead, but many applications can make good use of them due to synergies of cache sharing. Combining power, area, and timing results of McPAT with performance simulation of PARSEC benchmarks at the 22nm technology node for both common in-order and out-of-order manycore designs shows that when die cost is not taken into account clustering 8 cores together gives the best energy-delay product, whereas when cost is taken into account configuring clusters with 4 cores gives the best EDA2P and EDAP. We continue the investigation of problems concerning correlation clustering or clustering with qualitative information, which is a clustering formulation that has been studied recently [5, 7, 8, 3]. The basic setup here is that we are given as input a complete graph on n nodes (which correspond to nodes to be clustered) whose edges are labeled + (for similar pairs of items) and - (for dissimilar pairs of items). Thus we have only as input qualitative information on similarity and no quantitative distance measure between items. The quality of a clustering is measured in terms of its number of agreements, which is simply the number of edges it correctly classifies, that is the sum of number of - edges whose endpoints it places in different clusters plus the number of + edges both of whose endpoints it places within the same cluster.In this paper, we study the problem of finding clusterings that maximize the number of agreements, and the complementary minimization version where we seek clusterings that minimize the number of disagreements. We focus on the situation when the number of clusters is stipulated to be a small constant k. Our main result is that for every k, there is a polynomial time approximation scheme for both maximizing agreements and minimizing disagreements. (The problems are NP-hard for every k ≥ 2.) The main technical work is for the minimization version, as the PTAS for maximizing agreements follows along the lines of the property tester for Max k-CUT from [13].In contrast, when the number of clusters is not specified, the problem of minimizing disagreements was shown to be APX-hard [7], even though the maximization version admits a PTAS. Evaluating the performance of large compute clusters requires benchmarks with representative workloads. At Google, performance benchmarks are used to obtain performance metrics such as task scheduling delays and machine resource utilizations to assess changes in application codes, machine configurations, and scheduling algorithms. Existing approaches to workload characterization for high performance computing and grids focus on task resource requirements for CPU, memory, disk, I O, network, etc. Such resource requirements address how much resource is consumed by a task. However, in addition to resource requirements, Google workloads commonly include task placement constraints that determine which machine resources are consumed by tasks. Task placement constraints arise because of task dependencies such as those related to hardware architecture and kernel version. This paper develops methodologies for incorporating task placement constraints and machine properties into performance benchmarks of large compute clusters. Our studies of Google compute clusters show that constraints increase average task scheduling delays by a factor of 2 to 6, which often results in tens of minutes of additional task wait time. To understand why, we extend the concept of resource utilization to include constraints by introducing a new metric, the Utilization Multiplier (UM). UM is the ratio of the resource utilization seen by tasks with a constraint to the average utilization of the resource. UM provides a simple model of the performance impact of constraints in that task scheduling delays increase with UM. Last, we describe how to synthesize representative task constraints and machine properties, and how to incorporate this synthesis into existing performance benchmarks. Using synthetic task constraints and machine properties generated by our methodology, we accurately reproduce performance metrics for benchmarks of Google compute clusters with a discrepancy of only 13 in task scheduling delay and 5 in resource utilization. Diagnosis is the task of detecting fault occurrences in a partially observed system. Depending on the possible observations, a discrete-event system may be diagnosable or not. Active diagnosis aims at controlling the system to render it diagnosable. Past research has proposed solutions for this problem, but their complexity remains to be improved. Here, we solve the decision and synthesis problems for active diagnosability, proving that (1) our procedures are optimal with respect to computational complexity, and (2) the memory required for our diagnoser is minimal. We then study the delay between a fault occurrence and its detection by the diagnoser. We construct a memory-optimal diagnoser whose delay is at most twice the minimal delay, whereas the memory required to achieve optimal delay may be highly greater. We also provide a solution for parametrized active diagnosis, where we automatically construct the most permissive controller respecting a given delay. This paper considers the problem of clustering a partially observed unweighted graph---i.e., one where for some node pairs we know there is an edge between them, for some others we know there is no edge, and for the remaining we do not know whether or not there is an edge. We want to organize the nodes into disjoint clusters so that there is relatively dense (observed) connectivity within clusters, and sparse across clusters. We take a novel yet natural approach to this problem, by focusing on finding the clustering that minimizes the number of "disagreements"---i.e., the sum of the number of (observed) missing edges within clusters, and (observed) present edges across clusters. Our algorithm uses convex optimization; its basis is a reduction of disagreement minimization to the problem of recovering an (unknown) low-rank matrix and an (unknown) sparse matrix from their partially observed sum. We evaluate the performance of our algorithm on the classical Planted Partition Stochastic Block Model. Our main theorem provides sufficient conditions for the success of our algorithm as a function of the minimum cluster size, edge density and observation probability; in particular, the results characterize the tradeoff between the observation probability and the edge density gap. When there are a constant number of clusters of equal size, our results are optimal up to logarithmic factors. MapReduce clusters are usually multi-tenant (i.e., shared among multiple users and jobs) for improving cost and utilization. The performance of jobs in a multitenant MapReduce cluster is greatly impacted by the all-Map-to-all-Reduce communication, or Shuffle, which saturates the cluster's hard-to-scale network bisection bandwidth. Previous schedulers optimize Map input locality but do not consider the Shuffle, which is often the dominant source of traffic in MapReduce clusters. We propose ShuffleWatcher, a new multitenant MapReduce scheduler that shapes and reduces Shuffle traffic to improve cluster performance (throughput and job turn-around times), while operating within specified fairness constraints. ShuffleWatcher employs three key techniques. First, it curbs intra-job Map-Shuffle concurrency to shape Shuffle traffic by delaying or elongating a job's Shuffle based on the network load. Second, it exploits the reduced intra-job concurrency and the flexibility engendered by the replication of Map input data for fault tolerance to preferentially assign a job's Map tasks to localize the Map output to as few nodes as possible. Third, it exploits localized Map output and delayed Shuffle to reduce the Shuffle traffic by preferentially assigning a job's Reduce tasks to the nodes containing its Map output. ShuffleWatcher leverages opportunities that are unique to multi-tenancy, such overlapping Map with Shuffle across jobs rather than within a job, and trading-off intra-job concurrency for reduced Shuffle traffic. On a 100-node Amazon EC2 cluster running Hadoop, ShuffleWatcher improves cluster throughput by 39-46 and job turn-around times by 27-32 over three state-of-the-art schedulers.