905381
On the computational complexity of maintaining GPS clock in packet scheduling
Packet scheduling is an important mechanism to provide QoS guarantees in data networks. A scheduling algorithm generally consists of two functions: one estimates how the GPS (general processor sharing) clock progresses with respect to the real time; the other decides the order of serving packets based on an estimation of their GPS start/finish times. In this work, we answer important open questions concerning the computational complexity of performing the first function. We systematically study the complexity of computing the GPS virtual start/finish times of the packets, which has long been believed to be /spl Omega/(n) per packet but has never been either proved or refuted. We also answer several other related questions such as "whether the complexity can be lower if the only thing that needs to be computed is the relative order of the GPS finish times of the packets rather than their exact values?".
16173548
Robust traffic matrix estimation with imperfect information: making use of multiple data sources
Estimation of traffic matrices, which provide critical input for network capacity planning and traffic engineering, has recently been recognized as an important research problem. Most of the previous approaches infer traffic matrix from either SNMP link loads or sampled NetFlow records. In this work, we design novel inference techniques that, by statistically correlating SNMP link loads and sampled NetFlow records, allow for much more accurate estimation of traffic matrices than obtainable from either information source alone, even when sampled NetFlow records are available at only a subset of ingress. Our techniques are practically important and useful since both SNMP and NetFlow are now widely supported by vendors and deployed in most of the operational IP networks. More importantly, this research leads us to a new insight that SNMP link loads and sampled NetFlow records can serve as "error correction codes" to each other. This insight helps us to solve a challenging open problem in traffic matrix estimation, "How to deal with dirty data (SNMP and NetFlow measurement errors due to hardware/software/transmission problems)?" We design techniques that, by comparing notes between the above two information sources, identify and remove dirty data, and therefore allow for accurate estimation of the traffic matrices with the cleaned dat.We conducted experiments on real measurement data obtained from a large tier-1 ISP backbone network. We show that, when full deployment of NetFlow is not available, our algorithm can improve estimation accuracy significantly even with a small fraction of NetFlow data. More importantly, we show that dirty data can contaminate a traffic matrix, and identifying and removing them can reduce errors in traffic matrix estimation by up to an order of magnitude. Routing changes is another a key factor that affects estimation accuracy. We show that using them as the a priori, the traffic matrices can be estimated much more accurately than those omitting the routing change. To the best of our knowledge, this work is the first to offer a comprehensive solution which fully takes advantage of using multiple readily available data sources. Our results provide valuable insights on the effectiveness of combining flow measurement and link load measurement.
12382521
On the design and performance of prefix-preserving IP traffic trace anonymization
Even though real-world Internet traffic traces are crucial for network research, only a tiny percentage of traffic traces collected are made public. One major reason why traffic trace owners hesitate to make the traces publicly available is the concern that the confidential and private information may be inferred from the trace. In this paper we focus on the problem of anonymizing IP addresses in a trace. More specifically, we are interested in prefixpreserving anonymization in which the prefix relationship among IP addresses is preserved in the anonymized trace, making such a trace usable in situations where such prefix relationships are important. The goal of our work is two fold. First, we are interested in analyzing the security properties inherent in prefix-preserving IP address anonymization. Through the analysis of IP traffic traces, we investigate the effect of some types of attacks on the security of the prefix-preserving anonymization process. We also derive results for the optimum manner in which an attack should proceed which provides a bound on the performance of attacks in general. Second, we observe that an existing scheme used for prefix-preserving anonymization, TCPdpriv, has some drawbacks that limit its use in a large-scale, distributed setting. We develop an alternative cryptography-based, prefixpreserving anonymization technique to address these drawbacks while maintaining the same level of anonymity as TCPdpriv.
47532017
On fundamental tradeoffs between delay bounds and computational complexity in packet scheduling algorithms
We clarify, extend, and solve a long-standing open problem concerning the computational complexity for packet scheduling algorithms to achieve tight end-to-end delay bounds. We first focus on the difference between the time a packet finishes service in a scheduling algorithm and its virtual finish time under a GPS (General Processor Sharing) scheduler, called GPS-relative delay. We prove that, under a slightly restrictive but reasonable computational model, the lower bound computational complexity of any scheduling algorithm that guarantees O(1) GPS-relative delay bound is /spl Omega/(logn). We also discover that, surprisingly, the complexity lower bound remains the same even if the delay bound is relaxed to O(n/sup a/) for 0<a<1. This implies that the delay-complexity tradeoff curve is flat in the "interval" [O(1),O(n)). We later conditionally extend both complexity results (for O(1) or O(n/sup a/) delay) to a much stronger computational model, the linear decision tree. Finally, we show that the same complexity lower bounds are conditionally applicable to guaranteeing tight end-to-end delay bounds, if the delay bounds are provided through the Latency Rate (LR) framework.
10184291
Efficient and scalable query routing for unstructured peer-to-peer networks
Searching for content in peer-to-peer networks is an interesting and challenging problem. Queries in Gnutella-like unstructured systems that use flooding or random walk to search must visit O(n) nodes in a network of size n, thus consuming significant amounts of bandwidth. In this paper, we propose a query routing protocol that allows low bandwidth consumption during query forwarding using a low cost mechanism to create and maintain information about nearby objects. To achieve this, our protocol maintains a lightweight probabilistic routing table at each node that suggests the location of each object in the network. Following the corresponding routing table entries, a query can reach the destination in a small number of hops with high probability. However, maintaining routing tables in a large and highly dynamic network requires non-traditional mechanisms. We design a novel data structure called an exponentially decaying bloom filter (EDBF) that encodes such probabilistic routing tables in a highly compressed manner, and allows for efficient aggregation and propagation. The search primitives provided by our system can be used to search for single keys or multiple keywords with equal ease. Analytical modeling of our design predicts significant improvements in search efficiency, verified through extensive simulations in which we observed an order of magnitude reduction in query path length over previous proposals.
6305531
Shortest path queries in planar graphs
The problem of processing shortest pa th queries in graphs arises in application areas such as intelligent t ranspor ta t ion system (ITS), geographic information system (GIS), and robotics. In this paper, we present an efficient algorithmic solution for processing shortest pa th queries in undirected planar graphs with non-negative edge weights. Previous algorithms for this problem on planar graphs all have a tradeoff between the query t ime and the da ta structure space used by the solutions. The previously best known trade-off on an n-vertex planar graph G in the worst case is O(v/-r) t ime for a pa th length query and O(v/-r + L) t ime for report ing an actual shortest path, with a da ta structure of O(n2/x/~) space, where r is an integer parameter with 1 < r _< n and L is the number of edges on the output shortest path. We present a new scheme, called frame search, that exploits the graph planari ty in a novel fashion. Wi th this scheme, we build an improved da ta structure of O(n + pv/-r + p2/r) space (in O(n + p2/v/~ + pr 3/4) time), where p is the minimum cardinality of a face-covering of the planar embedding of G with 1 < p < O(n), and r is an integer parameter with 1 < r < p. This da ta structure enables us to process each length query in O(v/-rlog r + a(n)) t ime and report an actual shortest path in an addit ional O(L) time, where a(n) is the inverse of Ackermann's function. In the worst case, our approach reduces the previously best query t ime by a factor of up to O(n 1/4) if the same amount of space is used. Our technique can also be applied to improve the previous query algorithms for some geometric shortest pa th problems on the plane.
17909513
Determining an optimal penetration among weighted regions in two and three dimensions
We present efficient algorithms for solving the problem of computing an optimal penetration (a ray or a semi-ray) among weighted regions in 2-D and 3-D spaces. This problem finds applications in several areas, such as radiation therapy, geological exploration, and environmental engineering. Our algorithms are based on a combination of geometric techniques and optimization methods. Our geometric analysis shows that the d-D (d = 2, 3) optimal penetration problem can be reduced to solving O(n2(d−1)) instances of certain special types of non-linear optimization problems, where n is the total number of vertices of the regions. We also give implementation results of our 2-D algorithms.
15417765
The proof of a conjecture of Bouabdallah and Sotteau
Let G be a connected graph of order n. A routing in G is a set of n(n 1) fixed paths for all ordered pairs of vertices of G. The edge-forwarding index of G, (G), is the minimum of the maximum number of paths specified by a routing passing through any edge of G taken over all routings in G, and ,n is the minimum of (G) taken over all graphs of order n with maximum degree at most . To determine n 2p 1,n for 4p 2p/3 1 ≤ n ≤ 6p, A. Bouabdallah and D. Sotteau proposed the following conjecture in [On the edge forwarding index problem for small graphs, Networks 23 (1993), 249–255]. The set 3 {1, 2, . . . , (4p)/3} can be partitioned into 2p pairs plus singletons such that the set of differences of the pairs is the set 2 {1, 2, . . . , p}. This article gives a proof of this conjecture and determines that n 2p 1,n is equal to 5 if 4p 2p/3 1 ≤ n ≤ 6p and to 8 if 3p p/3 1 ≤ n ≤ 3p (3p)/5 for any p ≥ 2. © 2004 Wiley Periodicals, Inc. NETWORKS, Vol. 44(4), 292–296 2004
9706723
Efficient Job Scheduling Algorithms with Multi-Type Contentions
In this paper, we consider an interesting generalization of the classic job scheduling problem in which each job needs to compete not only for machines but also for other types of resources. The contentions among jobs for machines and for resources could interfere with each other, which complicates the problem dramatically. We present a family of approximation algorithms for solving several variants of the problem by using a generic algorithmic framework. Our algorithms achieve a constant approximation ratio (i.e., 3) when there is only one type of resources or certain dependency relation exists among multiple types of resources. When the r resources are unrelated, the approximation ratio of our algorithm becomes k+2, where k≤ r is a constant depending on the problem instance. As an application, we also show that our techniques can be easily applied to optical burst switching (OBS) networks to design more efficient wavelength scheduling algorithms.
757091
Efficient Job Scheduling Algorithms with Multi-type Contentions
In this paper, we consider an interesting generalization of the classic job scheduling problem in which each job needs to compete for not only machines but also other types of resources The contentions among jobs for machines and resources could interfere with each other, which complicates the problem dramatically We present a family of approximation algorithms for solving several variants of the problem by using a generic algorithmic framework Our algorithms achieve a constant approximation ratio (i.e., 3) if there is only one type of resources or certain dependency relation exists among multiple types of resources For the case that r unrelated resources are given, the approximation ratio of our algorithm becomes k + 2, where k ≤ r is a constant depending on the problem instance As an application, we also show that our techniques can be easily applied to optical burst switching (OBS) networks for deriving more efficient wavelength scheduling algorithms.