5875790
Algorithmic Ramifications of Prefetching in Memory Hierarchy
External Memory models, most notable being the I-O Model [3], capture the effects of memory hierarchy and aid in algorithm design. More than a decade of architectural advancements have led to new features not captured in the I-O model – most notably the prefetching capability. We propose a relatively simple Prefetch model that incorporates data prefetching in the traditional I-O models and show how to design algorithms that can attain close to peak memory bandwidth. Unlike (the inverse of) memory latency, the memory bandwidth is much closer to the processing speed, thereby, intelligent use of prefetching can considerably mitigate the I-O bottleneck. For some fundamental problems, our algorithms attain running times approaching that of the idealized Random Access Machines under reasonable assumptions. Our work also explains the significantly superior performance of the I-O efficient algorithms in systems that support prefetching compared to ones that do not.
31766769
Improved selection in totally monotone arrays
This paper's main result is an -time algorithm for computing the kth smallest entry in each row of an m×n totally monotone array. (A two-dimensional array A={a[i, j]} is totally monotone if for all i1<i2 and j1<j2, a[i1, j1]<a[i1, j2] implies a[i2, j1]<a[i2, j2].) For large values of k (in particular, for k=⌈n/2⌉), this algorithm is significantly faster than the O(k(m + n))-time algorithm for the same problem due to Kravets and Park. An immediate consequence of this result is an O(n3/2lg1/2 n)-time algorithm for computing the kth nearest neighbor of each vertex of a convex n-gon. In addition to the main result, we also give an O(n lg m)-time algorithm for computing an approximate median in each row of an m×n totally monotone array; this approximate median is an entry whose rank in its row lies between ⌊n/4⌋ and ⌈3n/4⌉ − 1.
41531267
A linear time algorithm for approximate 2-means clustering
Matousek [Discrete Comput. Geom. 24 (1) (2000) 61-84] designed an O(nlogn) deterministic algorithm for the approximate 2-means clustering problem for points in fixed dimensional Euclidean space which had left open the possibility of a linear time algorithm. In this paper, we present a simple randomized algorithm to determine an approximate 2-means clustering of a given set of points in fixed dimensional Euclidean space, with constant probability, in linear time.We first approximate the mean of the larger cluster using random sampling. We then show that the problem can be reduced to a set of lines, on which it can be solved by carefully pruning away points of the larger cluster and randomly sampling on the remaining points to obtain an approximate to the mean of the smaller cluster.
11169442
Linear Time Algorithms for Clustering Problems in Any Dimensions
We generalize the k-means algorithm presented by the authors [14] and show that the resulting algorithm can solve a larger class of clustering problems that satisfy certain properties (existence of a random sampling procedure and tightness). We prove these properties for the k-median and the discrete k-means clustering problems, resulting in O(2(k/e)O(1)dn) time (1+e)-approximation algorithms for these problems. These are the first algorithms for these problems linear in the size of the input (nd for n points in d dimensions), independent of dimensions in the exponent, assuming k and e to be fixed. A key ingredient of the k-median result is a (1+e)-approximation algorithm for the 1-median problem which has running time O(2(1/e)O(1)d). The previous best known algorithm for this problem had linear running time.
13425332
A generalization of the 0-1 principle for sorting
The traditional zero-one principle for sorting networks states that "if a network with n input lines sorts all 2n binary sequences into nondecreasing order, then it will sort any arbitrary sequence of n numbers into nondecreasing order". We generalize this to the situation when a network sorts almost all binary sequences and relate it to the behavior of the sorting network on arbitrary inputs. We also present an application to mesh sorting.
1068367
An Efficient Output-Size Sensitive Parallel Algorithm for Hidden-Surface Removal for Terrains
Abstract. We describe an efficient parallel algorithm for hidden-surface removal for terrain maps. The algorithm runs in O(log 4 n) steps on the CREW PRAM model with a work bound of O((n+k) \polylog ( n)) where n and k are the input and output sizes, respectively. In order to achieve the work bound we use a number of techniques, among which our use of persistent data structures is somewhat novel in the context of parallel algorithms.
15974834
Learning Pareto-optimal Solutions in 2x2 Conflict Games
Multiagent learning literature has investigated iterated two-player games to develop mechanisms that allow agents to learn to converge on Nash Equilibrium strategy profiles. Such equilibrium configurations imply that no player has the motivation to unilaterally change its strategy. Often, in general sum games, a higher payoff can be obtained by both players if one chooses not to respond myopically to the other player. By developing mutual trust, agents can avoid immediate best responses that will lead to a Nash Equilibrium with lesser payoff. In this paper we experiment with agents who select actions based on expected utility calculations that incorporate the observed frequencies of the actions of the opponent(s). We augment these stochastically greedy agents with an interesting action revelation strategy that involves strategic declaration of one's commitment to an action to avoid worst-case, pessimistic moves. We argue that in certain situations, such apparently risky action revelation can indeed produce better payoffs than a non-revealing approach. In particular, it is possible to obtain Pareto-optimal Nash Equilibrium outcomes. We improve on the outcome efficiency of a previous algorithm and present results over the set of structurally distinct two-person two-action conflict games where the players' preferences form a total order over the possible outcomes. We also present results on a large number of randomly generated payoff matrices of varying sizes and compare the payoffs of strategically revealing learners to payoffs at Nash equilibrium.
47152006
Optimal proxy cache allocation for efficient streaming media distribution
We address the problem of efficiently streaming a set of heterogeneous videos from a remote server through a proxy to multiple asynchronous clients so that they can experience playback with low startup delays. We determine the optimal proxy prefix cache allocation to the videos that minimizes the aggregate network bandwidth cost. We integrate proxy caching with traditional server-based reactive transmission schemes such as hatching, patching and stream merging to develop a set of proxy-assisted delivery schemes. We quantitatively explore the impact of the choice of transmission scheme, cache allocation policy, proxy cache size, and availability of unicast versus multicast capability, on the resulting transmission cost. Our evaluations show that even a relatively small prefix cache (10%-20% of the video repository) is sufficient to realize substantial savings in transmission cost. We find that carefully designed proxy-assisted reactive transmission schemes can produce significant cost savings even in a predominantly unicast environment such as the Internet.
1578205
Broadcast on demand: efficient and timely dissemination of data in mobile environments
The demand for efficient scalable and cost effective mobile information access systems is rapidly growing. Radiofrequency broadcast plays a major role in mobile computing, and there is a need to provide service models for broadcasting information according to mobile users' needs. The authors present a model called broadcast on demand (BoD), which provides timely broadcasts according to requests from users. Compared to static broadcast, this approach has a different emphasis: it is based on a demand driven framework, aimed at satisfying the temporal constraints of the requests, and uses scheduling techniques at the server side to utilize the limited bandwidth dynamically and efficiently. Several broadcast transmission scheduling policies for BoD are examined. The study indicates that EDF-based policies combined with batching of requests achieve good performance. The results show that BoD is successful in satisfying the temporal constraints of the requests and is a viable service model for wireless broadcast stations.
2290480
Optimal multicast smoothing of streaming video over an internetwork
A number of applications such as internet video broadcasts, corporate telecasts, distance learning etc. require transmission of streaming video to multiple simultaneous users across an internetwork. The high bandwidth requirements coupled with the multi-timescale burstiness of compressed video make it a challenging problem to provision network resources for transmitting streaming multimedia. For such applications to become affordable and ubiquitous, it is necessary to develop scalable techniques which can efficiently deliver streaming video to multiple heterogeneous clients across a heterogeneous internetwork. We propose using multicasting of smoothed video and differential caching of the video at intermediate nodes in the distribution tree, as techniques for reducing the network bandwidth requirements of such dissemination. We formulate the multicast smoothing problem, and develop an algorithm for computing the set of optimally smoothed transmission schedules for the tree (such that the transmission schedule along each link in the tree has the lowest peak rate and rate variability for any feasible transmission schedule for that link) given a buffer allocation to the different nodes in the tree. We also develop an algorithm to compute the minimum total buffer allocation to the entire tree and the corresponding allocation to each node, such that feasible transmission is possible to all the clients, when the tree has heterogeneous rate constraints. MPEG-2 trace-driven performance evaluations indicate that there are substantial benefits from multicast smoothing and differential caching. For example, the optimal multicast smoothing can reduce the total transmission bandwidth requirements in the distribution tree by more than a factor of 3 as compared to multicasting the unsmoothed stream.
2225573
Integrated scheduling of multimedia and hard real-time tasks
An integrated platform which is capable of meeting the requirements of both traditional real-time control processing and multimedia processing has enormous potential for accommodating various kinds of new applications. However, except for the simplest of situations, few, if any, research or commercial systems successfully provide architectural and OS mechanisms which can efficiently support both hard real-time computation and multimedia soft real-time computation. The authors propose a multimedia server execution on multiprocessor real-time operating systems to provide different classes of guarantee to support both types of processing. The multimedia server supports multiple periodic multimedia streams with a capability for graceful QoS degradation during system overload. They (i) develop several multimedia server scheduling algorithms, (ii) evaluate the performance of these algorithms, and (iii) discuss realistic system implementation issues on the SGI IRIX/REACT/PRO operating system.