Dynamic storage allocation is the problem of packing given axis-aligned rectangles into a horizontal strip of minimum height by sliding the rectangles vertically but not horizontally. Where L= is the maximum sum of heights of rectangles that intersect any vertical line and OPT is the minimum height of the enclosing strip, it is obvious that $\ensuremath{\text{\it OPT}}\ge \ensuremath{\text{\it LOAD}}$; previous work showed that $\ensuremath{\text{\it OPT}}\le 3\cdot LOAD. We continue the study of the relationship between OPT and LOAD, proving that OPT=L+O((h max /L) 1/7 )L, where h max is the maximum job height. Conversely, we prove that for any $\epsilon > 0$, there exists a c>0 such that for all sufficiently large integers $h_{\max}$, there is a dynamic storage allocation instance with maximum job height $h_{\max}$, maximum load at most L, and $\ensuremath{\text{\it OPT}}\geq L+c(h_{\max}/L)^{1/2+\epsilon}L$, for infinitely many integers L. En route, we construct several new polynomial-time approximation algorithms for dynamic storage allocation, including a $(2+\epsilon)$-approximation algorithm for the general case and polynomial-time approximation schemes for several natural special cases.

DYNAMIC STORAGE ALLOCATION is the problem of packing given axis-aligned rectangles into a horizontal strip of minimum height by sliding the rectangles vertically but not horizontally. Where L=LOAD is the maximum sum of heights of rectangles that intersect any vertical line and OPT is the minimum height of the enclosing strip, it is obvious that OPT≥LOAD; previous work showed that OPT≤ 3• LOAD. We continue the study of the relationship between OPT and LOAD, proving that OPT=L+O((hmax/L)1/7)L, where hmax is the maximum job height. Conversely, we prove that for any ε>0, there exists a c>0 such that for all sufficiently large integers hmax, there is a DYNAMIC STORAGE ALLOCATION instance with maximum job height hmax, maximum load at most L, and OPT≥ L+c(hmax/L)1/2+εL, for infinitely many integers L. En route, we construct several new polynomial-time approximation algorithms for DYNAMIC STORAGE ALLOCATION.

Engineering a large IP backbone network without an accurate network-wide view of the traffic demands is challenging. Shifts in user behavior, changes in routing policies, and failures of network elements can result in significant (and sudden) fluctuations in load. We present a model of traffic demands to support traffic engineering and performance debugging of large Internet service provider networks. By defining a traffic demand as a volume of load originating from an ingress link and destined to a set of egress links, we can capture and predict how routing affects the traffic traveling between domains. To infer the traffic demands, we propose a measurement methodology that combines flow-level measurements collected at all ingress links with reachability information about all egress links. We discuss how to cope with situations where practical considerations limit the amount and quality of the necessary data. Specifically, we show how to infer interdomain traffic demands using measurements collected at a smaller number of edge links-the peering links connecting to neighboring providers. We report on our experiences in deriving the traffic demands in the AT&T IP Backbone, by collecting, validating, and joining very large and diverse sets of usage, configuration, and routing data over extended periods of time. The paper concludes with a preliminary analysis of the observed dynamics of the traffic demands and a discussion of the practical implications for traffic engineering.

Engineering a large IP backbone network without an accurate, network-wide view of the traffic demands is challenging. Shifts in user behavior, changes in routing policies, and failures of network elements can result in significant (and sudden) fluctuations in load. In this paper, we present a model of traffic demands to support traffic engineering and performance debugging of large Internet Service Provider networks. By defining a traffic demand as a volume of load originating from an ingress link and destined to a set of egress links, we can capture and predict how routing affects the traffic traveling between domains. To infer the traffic demands, we propose a measurement methodology that combines flow-level measurements collected at all ingress links with reachability information about all egress links. We discuss how to cope with situations where practical considerations limit the amount and quality of the necessary data. Specifically, we show how to infer interdomain traffic demands using measurements collected at a smaller number of edge links --- the peering links connecting to neighboring providers. We report on our experiences in deriving the traffic demands in the AT&T IP Backbone, by collecting, validating, and joining very large and diverse sets of usage, configuration, and routing data over extended periods of time. The paper concludes with a preliminary analysis of the observed dynamics of the traffic demands and a discussion of the practical implications for traffic engineering.

Competitive on-line algorithms for data management in a network of processors are studied in this paper. A data object such as a file or a page of virtual memory is to be read and updated by various processors in the network. The goal is to minimize the communication costs incurred in serving a sequence of such requests. Distributed data management on important classes of networks---trees and bus-based networks---are studied. Optimal algorithms with constant competitive ratios and matching lower bounds are obtained. Our algorithms use different interesting techniques, such as work functions [Chrobak and Larmore, Proc. DIMACS Workshop on On-Line Algorithms, AMS, 1991, pp. 11--64] and "factoring."

Beigel, Reingold, and Spielman (J. Comput. System Sci.50, 191–202 (1995)) showed that PP is closed under intersection and a variety of special cases of polynomial-time truth-table closure. We extend their techniques to show that PP is closed under general polynomial-time truth-table reductions. We also show that PP is closed under constant-round truth-table reductions.

Optimum off-line algorithms for the list update problem are investigated. The list update problem involves implementing a dictionary of items as a linear list. Several characterizations of optimum algorithms are given; these lead to optimum algorithm which runs in time Θ2n(n − 1)!m, where n is the length of the list and m is the number of requests. The previous best algorithm, an adaptation of a more general algorithm due to Manasse et al. (1988), runs in time Θ(n!)2m.

Next generation wide area networks will be connection-oriented, with data-link layer connectivity being provided by asynchronous transfer mode (ATM). For the huge existing investment in current IP networks such as the Internet to remain useful, one must devise mechanisms to carry IP traffic over ATM networks. A fundamental issue is to devise holding policies for virtual circuits carrying datagrams. The authors consider two pricing schemes, the first is a likely pricing scheme of future ATM networks, while the second is based on characteristics of current networks. For each pricing scheme, the authors devise a simple holding policy that adapts to the characteristics of the IP traffic. The authors simulate their policies on actual network traffic and find that they perform significantly better than previous policies.

In this seminal paper on probabilistic Turing machines, Gill asked whether the class PP is closed under intersection and union. We give a positive answer to this question. We also show that PP is closed under a variety of polynomial-time truth-table reductions. Consequences in complexity theory include the definite collapse and (assuming P ≠ PP) separation of certain query hierarchies over PP. Similar techniques allow us to combine several threshold gates into a single threshold gate. Consequences in the study of circuits include the simulation of circuits with a small number of threshold gates by circuits having only a single threshold gate at the root (perceptrons) and a lower bound on the number of threshold gates that are needed to compute the parity function.

When carrying Internet protocol (IP) traffic over an asynchronous transfer mode (ATM) network, the ATM adaptation layer must determine how long to hold a virtual circuit opened to carry an IP datagram. We present a formal statement of the problem and carry out a detailed empirical examination of various holding time policies taking into account the issue of network pricing. We offer solutions for two natural pricing models, the first being a likely pricing model of future ATM networks, while the second is based on characteristics of current networks. For each pricing model, we study a variety of simple nonadaptive policies as well as easy to implement policies that adapt to the characteristics of the IP traffic. We simulate our policies on actual network traffic, and find that policies based on least recently used (LRU) perform well, although the best adaptive policies provide a significant improvement over LRU.>

Next generation wide area network are very likely to use connection-oriented protocols such as Asynchronous Transfer Mode (ATM). For the huge existing investment in current IP networks such as the Internet to remain useful, me must devise mechanisms to carry IP traffic over connection-oriented networks. A basic issue is to devise holding policies for virtual circuits carrying datagrams. In this paper we consider two variants of the paging problem that arise in the design of such holding policies. In the IP-paging problem the page inter-request times are chosen according to independent distributions. For this model we construct a very simple deterministic algorithm whose page fault rate is at most 5 times that of the best online algorithm (that knows the inter-request time distributions). We also show that some natural algorithms for this problem do not have constant competitive ratio. In distributional paging the inter-request time distributions may be dependent, and hence any probabilistic model of page request sequences can be represented. We construct a simple randomized algorithm whose page fault rate is at most 4 times that of the best online algorithm.>

In his seminal paper on probabilistic Turing machines, Gill [13] asked whether the class PP is closed under intersection and union. We give a positive answer to this question. We also show that PP is closed under a variety of polynomial-time truth-table reductions. Consequences in complexity theory include the definite collapse and (assuming P 6= PP) separation of certain query hierarchies over PP. Similar techniques allow us to combine several threshold gates into a single threshold gate. Consequences in the study of circuits include the simulation of circuits with a small number of threshold gates by circuits having only a single threshold gate at the root (perceptrons), and a lower bound on the number of threshold gates needed to compute the parity function. 1. Introduction The class PP was defined in 1972 by John Gill [13, 14] and independently by Janos Simon [26] in 1974. PP is the class of languages accepted by a polynomial-time bounded nondeterministic Turing machine t...