Eric Torng

Optimal time-critical scheduling via resource augmentation

AbstractWe consider two fundamental problems in dynamic scheduling: scheduling to meet deadlines in a preemptive multiprocessor setting, and scheduling to provide good response time in a number of scheduling environments. When viewed from the perspective of traditional worst-case analysis, no good on-line algorithms exist for these problems, and for some variants no good off-line algorithms exist unless P = NP .We study these problems using a relaxed notion of competitive analysis, introduced by Kalyanasundaram and Pruhs, in which the on-line algorithm is allowed more resources than the optimal off-line algorithm to which it is compared. Using this approach, we establish that several well-known on-line algorithms, that have poor performance from an absolute worst-case perspective, are optimal for the problems in question when allowed moderately more resources. For optimization of average flow time, these are the first results of any sort, for any NP -hard version of the problem, that indicate that it might be possible to design good approximation algorithms.

TCAM Razor: a systematic approach towards minimizing packet classifiers in TCAMs

Packet classification is the core mechanism that enables many networking services on the Internet such as firewall packet filtering and traffic accounting. Using ternary content addressable memories (TCAMs) to perform high-speed packet classification has become the de facto standard in industry. TCAMs classify packets in constant time by comparing a packet with all classification rules of ternary encoding in parallel. Despite their high speed, TCAMs suffer from the well-known range expansion problem. As packet classification rules usually have fields specified as ranges, converting such rules to TCAM-compatible rules may result in an explosive increase in the number of rules. This is not a problem if TCAMs have large capacities. Unfortunately, TCAMs have very limited capacity, and more rules mean more power consumption and more heat generation for TCAMs. Even worse, the number of rules in packet classifiers has been increasing rapidly with the growing number of services deployed on the Internet. In this paper, we consider the following problem: given a packet classifier, how can we generate another semantically equivalent packet classifier that requires the least number of TCAM entries? In this paper, we propose a systematic approach, the TCAM Razor, that is effective, efficient, and practical. In terms of effectiveness, TCAM Razor achieves a total compression ratio of 29.0%, which is significantly better than the previously published best result of 54%. In terms of efficiency, our TCAM Razor prototype runs in seconds, even for large packet classifiers. Finally, in terms of practicality, our TCAM Razor approach can be easily deployed as it does not require any modification to existing packet classification systems, unlike many previous range encoding schemes.

A Better Algorithm for an Ancient Scheduling Problem

We consider the online multiprocessor scheduling problem first considered by Graham in 1966 which can be formulated as the following online load-balancing problem: a set of jobs arrive on-line, and each job must be immediately and irrevocably assigned to one ofmidentical machines without any knowledge of future jobs. The goal of the load balancer is to minimize the maximum load on any machine. We present the algorithm CHASM?that outperforms all previously published algorithms for anym?8 and has a competitive ratio of at most 1.945 for allm(the best known lower bound is 1.837). We show that our analysis of CHASM?is almost tight by presenting a lower bound of 1.9378 on its competitive ratio for largem. We also explore some of the trade-offs between any algorithms worst case and average case performance, and we consider the case when jobs have finite, unknown duration.

Bit weaving: a non-prefix approach to compressing packet classifiers in TCAMs

Ternary content addressable memories (TCAMs) have become the de facto standard in industry for fast packet classification. Unfortunately, TCAMs have limitations of small capacity, high power consumption, high heat generation, and high cost. The well-known range expansion problem exacerbates these limitations as each classifier rule typically has to be converted to multiple TCAM rules. One method for coping with these limitations is to use compression schemes to reduce the number of TCAM rules required to represent a classifier. Unfortunately, all existing compression schemes only produce prefix classifiers. Thus, they all miss the compression opportunities created by non-prefix ternary classifiers. In this paper, we propose bit weaving, the first non-prefix compression scheme. Bit weaving is based on the observation that TCAM entries that have the same decision and whose predicates differ by only one bit can be merged into one entry by replacing the bit in question with . Bit weaving consists of two new techniques, bit swapping and bit merging, to first identify and then merge such rules together. The key advantages of bit weaving are that it runs fast, it is effective, and it is composable with other TCAM optimization methods as a pre/post-processing routine. We implemented bit weaving and conducted experiments on both real-world and synthetic packet classifiers. Our experimental results show the following: 1) bit weaving is an effective standalone compression technique (it achieves an average compression ratio of 23.6%); 2) bit weaving finds compression opportunities that other methods miss. Specifically, bit weaving improves the prior TCAM optimization techniques of TCAM Razor and Topological Transformation by an average of 12.8% and 36.5%, respectively.

Firewall Compressor: An Algorithm for Minimizing Firewall Policies

A firewall is a security guard placed between a private network and the outside Internet that monitors all incoming and outgoing packets. The function of a firewall is to examine every packet and decide whether to accept or discard it based upon the firewalls policy. This policy is specified as a sequence of (possibly conflicting) rules. When a packet comes to a firewall, the firewall searches for the first rule that the packet matches, and executes the decision of that rule. With the explosive growth of Internet-based applications and malicious attacks, the number of rules in firewalls have been increasing rapidly, which consequently degrades network performance and throughput. In this paper, we propose Firewall Compressor, a framework that can significantly reduce the number of rules in a firewall while keeping the semantics of the firewall unchanged. We make three major contributions in this paper. First, we propose an optimal solution using dynamic programming techniques for compressing one-dimensional firewalls. Second, we present a systematic approach to compressing multi-dimensional firewalls. Last, we conducted extensive experiments to evaluate Firewall Compressor. In terms of effectiveness, Firewall Compressor achieves an average compression ratio of 52.3% on real- life rule sets. In terms of efficiency, Firewall Compressor runs in seconds even for a large firewall with thousands of rules. Moreover, the algorithms and techniques proposed in this paper are not limited to firewalls. Rather, they can be applied to other rule-based systems such as packet filters on Internet routers.

A unified analysis of paging and caching

Abstract. Paging (caching) is the problem of managing a two-level memory hierarchy in order to minimize the time required to process a sequence of memory accesses. In order to measure this quantity, which we refer to as the total memory access time, we define the system parameter miss penalty to represent the extra time required to access slow memory. We also introduce the system parameter page size. In the context of paging, miss penalty is quite large, so most previous studies of on-line paging have implicitly set miss penalty =∞ in order to simplify the model. We show that this seemingly insignificant simplification substantially alters the precision of derived results. For example, previous studies have essentially ignored page size. Consequently, we reintroduce the miss penalty and page size parameters to the paging problem and present a more accurate analysis of on-line paging (and caching). We validate using this more accurate model by deriving intuitively appealing results for the paging problem which cannot be derived using the simplified model. First, we present a natural, quantifiable definition of the amount of locality of reference in any access sequence. We also point out that the amount of locality of reference in an access sequence should depend on page size among other factors. We then show that deterministic and randomized marking algorithms such as the popular least recently used (LRU) algorithm achieve constant competitive ratios when processing typical access sequences which exhibit significant locality of reference; this represents the first competitive analysis result which (partially) explains why LRU performs as well as it is observed to in practice. Next, we show that finite lookahead can be used to obtain algorithms with improved competitive ratios. In particular, we prove that modified marking algorithms with sufficient lookahead achieve competitive ratios of 2. This is in stark contrast to the simplified model where lookahead cannot be used to obtain algorithms with improved competitive ratios. We conclude by using competitive analysis to evaluate the benefits of increasing associativity in caches. We accomplish this by specifying an algorithm and varying the system configuration rather than the usual process of specifying the system configuration and varying the algorithm.

TCAM Razor: A Systematic Approach Towards Minimizing Packet Classifiers in TCAMs

Packet classification is the core mechanism that enables many networking services on the Internet such as firewall packet filtering and traffic accounting. Using ternary content addressable memories (TCAMs) to perform high-speed packet classification has become the de facto standard in industry. TCAMs classify packets in constant time by comparing a packet with all classification rules of ternary encoding in parallel. Despite their high speed, TCAMs suffer from the well-known range expansion problem. As packet classification rules usually have fields specified as ranges, converting such rules to TCAM-compatible rules may result in an explosive increase in the number of rules. This is not a problem if TCAMs have large capacities. Unfortunately, TCAMs have very limited capacity, and more rules means more power consumption and more heat generation for TCAMs. Even worse, the number of rules in packet classifiers have been increasing rapidly with the growing number of services deployed on the internet. To address the range expansion problem of TCAMs, we consider the following problem: given a packet classifier, how can we generate another semantically equivalent packet classifier that requires the least number of TCAM entries? In this paper, we propose a systematic approach, the TCAM Razor, that is effective, efficient, and practical. In terms of effectiveness, our TCAM Razor prototype achieves a total compression ratio of 3.9%, which is significantly better than the previously published best result of 54%. In terms of efficiency, our TCAM Razor prototype runs in seconds, even for large packet classifiers. Finally, in terms of practicality, our TCAM Razor approach can be easily deployed as it does not require any modification to existing packet classification systems, unlike many previous range expansion solutions.

Mobile Relay Configuration in Data-Intensive Wireless Sensor Networks

Wireless Sensor Networks (WSNs) are increasingly used in data-intensive applications such as microclimate monitoring, precision agriculture, and audio/video surveillance. A key challenge faced by data-intensive WSNs is to transmit all the data generated within an applications lifetime to the base station despite the fact that sensor nodes have limited power supplies. We propose using low-cost disposable mobile relays to reduce the energy consumption of data-intensive WSNs. Our approach differs from previous work in two main aspects. First, it does not require complex motion planning of mobile nodes, so it can be implemented on a number of low-cost mobile sensor platforms. Second, we integrate the energy consumption due to both mobility and wireless transmissions into a holistic optimization framework. Our framework consists of three main algorithms. The first algorithm computes an optimal routing tree assuming no nodes can move. The second algorithm improves the topology of the routing tree by greedily adding new nodes exploiting mobility of the newly added nodes. The third algorithm improves the routing tree by relocating its nodes without changing its topology. This iterative algorithm converges on the optimal position for each node given the constraint that the routing tree topology does not change. We present efficient distributed implementations for each algorithm that require only limited, localized synchronization. Because we do not necessarily compute an optimal topology, our final routing tree is not necessarily optimal. However, our simulation results show that our algorithms significantly outperform the best existing solutions.

Distributed Cooperative Caching in Social Wireless Networks

This paper introduces cooperative caching policies for minimizing electronic content provisioning cost in Social Wireless Networks (SWNET). SWNETs are formed by mobile devices, such as data enabled phones, electronic book readers etc., sharing common interests in electronic content, and physically gathering together in public places. Electronic object caching in such SWNETs are shown to be able to reduce the content provisioning cost which depends heavily on the service and pricing dependences among various stakeholders including content providers (CP), network service providers, and End Consumers (EC). Drawing motivation from Amazons Kindle electronic book delivery business, this paper develops practical network, service, and pricing models which are then used for creating two object caching strategies for minimizing content provisioning costs in networks with homogenous and heterogeneous object demands. The paper constructs analytical and simulation models for analyzing the proposed caching strategies in the presence of selfish users that deviate from network-wide cost-optimal policies. It also reports results from an Android phone-based prototype SWNET, validating the presented analytical and simulation results.

Split: Optimizing Space, Power, and Throughput for TCAM-Based Classification

Using Ternary Content Addressable Memories (TCAMs) to perform high-speed packet classication has become the de facto standard in industry because TCAMs facilitate constant time classication by comparing packet elds against ternary encoded rules in parallel. Despite their high speed, TCAMs have limitations of small capacity, large power consumption, and relatively slow access times. One reason TCAM-based packet classiers are so large is the multiplicative eect inherent in representing d-dimensional classiers in TCAMs. To address the multiplicative effect, we propose the TCAM Split architecture, where a d-dimensional classier is split into k = 2 low dimensional classiers, each of which is stored on its own small TCAM. A d-dimensional lookup is split into k low dimensional, pipe-lined lookups with one lookup on each chip. Our experimental results with real-life classiers show that TCAM Split reduces classier size by 84% using only two small TCAM chips, this increases to 93% if we use ve small TCAM chips.