15892344
Design of a novel statistics counter architecture with optimal space and time efficiency
The problem of how to efficiently maintain a large number (say millions) of statistics counters that need to be incremented at very high speed has received considerable research attention recently. This problem arises in a variety of router management algorithms and data streaming algorithms, where a large array of counters is used to track various network statistics and to implement various counting sketches respectively. While fitting these counters entirely in SRAM meets the access speed requirement, a large amount of SRAM may be needed with a typical counter size of 32 or 64 bits, and hence the high cost. Solutions proposed in recent works have used hybrid architectures where small counters in SRAM are incremented at high speed, and occasionally written back ("flushed") to larger counters in DRAM. Previous solutions have used complex schedulers with tree-like or heap data structures to pick which counters in SRAM are about to overflow, and flush them to the corresponding DRAM counters.In this work, we present a novel hybrid SRAM/DRAM counter architecture that consumes much less SRAM and has a much simpler design of the scheduler than previous approaches. We show, in fact, that our design is optimal in the sense that for a given speed difference between SRAM and DRAM, our design uses the theoretically minimum number of bits per counter in SRAM. Our design uses a small write-back buffer (in SRAM) that stores indices of the overflowed counters (to be flushed to DRAM) and an extremely simple randomized algorithm to statistically guarantee that SRAM counters do not overflow in bursts large enough to fill up the write-back buffer even in the worst case. The statistical guarantee of the algorithm is proven using a combination of worst case analysis for characterizing the worst case counter increment sequence and a new tail bound theorem for bounding the probability of filling up the write-back buffer. Experiments with real Internet traffic traces show that the buffer size required in practice is significantly smaller than needed in the worst case.
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.
16814075
On algebraic construction of Gallager and circulant low-density parity-check codes
This correspondence presents three algebraic methods for constructing low-density parity-check (LDPC) codes. These methods are based on the structural properties of finite geometries. The first method gives a class of Gallager codes and a class of complementary Gallager codes. The second method results in two classes of circulant-LDPC codes, one in cyclic form and the other in quasi-cyclic form. The third method is a two-step hybrid method. Codes in these classes have a wide range of rates and minimum distances, and they perform well with iterative decoding.
195710562
On fundamental tradeoffs between delay bounds and computational complexity in packet scheduling algorithms
In this work, we clarify, extend and solve an 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 Ω (log 2 n) (widely believed as a "folklore theorem" but never proved). We also discover that, surprisingly, the complexity lower bound remains the same even if the delay bound is relaxed to O(na) for 0‹a⋵1. This implies that the delay-complexity tradeoff curve is "flat" in the "interval" [O(1), O(n)). We later extend both complexity results (for O(1) or O(na) delay) to a much stronger computational model. Finally, we show that the same complexity lower bounds are conditionally applicable to guaranteeing tight end-to-end delay bounds. This is done by untangling the relationship between the GPS-relative delay bound and the end-to-end delay bound.
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.
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?".
2254306
An efficient direct approach for computing shortest rectilinear paths among obstacles in a two-layer interconnection model
In this paper, we present a direct approach for routing a shortest rectilinear path between two points among a set of rectilinear obstacles in a two-layer interconnection model that is used for VLSI routing applications. The previously best known direct approach for this problem takes O(nlog^2n) time and O(nlogn) space, where n is the total number of obstacle edges. By using integer data structures and an implicit graph representation scheme (i.e., a generalization of the distance table method), we improve the time bound to O(nlog^3^/^2n) while still maintaining the O(nlogn) space bound. Comparing with the indirect approach for this problem, our algorithm is simpler to implement and is probably faster for a quite large range of input sizes.
2025275
Optimizing the sum of linear fractional functions and applications
1 I n t r o d u c t i o n . The problem of optimizing the sum of linear fractional functions (SOLF) is defined as follows: max f(Zl,...,Xd)= ~ [ : 7 : ~ d ) (Xl ..... z~t)ES i=1 ~ a r t m e n t of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN 46556, USA, {chen,odaescu,xwu,jxu}@cse.nd.edu. This research was supported in part by the National Science Foundation under Grant CCR-9623585. tThe work of this author was supported in part by a fellowship of the Center for Applied Mathematics, University of Notre Dame, Notre Dame, Indiana, USA. t Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, 2-12-1 O-okayama, Meguro-ku, Tokyo 152, Japan, daiOis.titech.ac.jp. Grant-in-Aid of Ministry of Science, Culture and Education of Japan, No. 10780274. §Department of Architecture and Architectural Systems, Graduate School of Engineering, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto, 606-8501 Japan, naoki~archi.kyoto-u.ac.jp. Partially supported by Grant-inAid for Scientific Research on Priority Areas (B) by the Ministry of Education, Science, Sports and Culture of Japan. IThe work of this author was supported in part by a fellowship of the Center for Applied Mathematics, and by a summer graduate research fellowship of the Graduate School, University of Notre Dame, Notre Dame, Indiana, USA. such that for each i = 1 , 2 , . . . , m , ni(Xl,...,Xd) and di(Xl,...,Xd) are linear functions in a fixed d-D space ]~d, di (x t , . . . ,Xd) ~ 0 for any (Xl , . . . ,Xd) E S, the feasible domain S is defined by n linear constraints (i.e., half-spaces in Rd), and S ~ ¢. Each linear fractional term ~(~1 ..... ~ ) ddxl,...,z~) is called a ratio. The SOLF problem appears in the algorithmic solutions for several geometric optimization problems. In layered manufacturing, Majhi et al. [17], [18] showed that the length-optimal supports for a simple nonconvex polygon can be obtained by solving the 1-D SOLF problem on an interval. Arkin et al. [1] formulated the problem of finding a minimum-area starshaped or monotone polygon that contains a simple polygon, which appears in material layout [1], [8], [21] (e.g., cloth manufacturing) and manufacturing [18], as one of optimizing the sum of 2-D fractional polynomials of degrees 3 and 2 under linear constraints. We will show that the objective function of this problem can actually be simplified to the 2-D SOLF form. For the problem of finding optimal penetrations among weighted regions [5], we shall show tha t the L1 and Leo versions of this problem have the 2-D SOLF problem as a key subproblem. The SOLF problem also arises in other areas. For example, in combinatorial optimization, a class of problems on finding a structure with the maximum (or minimum) mean-weight cost can be solved by optimizing some linear fractional functions [23]. In operations research, it was shown in [11], [24] that many economic applications (e.g., maximization of productivity, return on investment, and return/risk) can be reduced to solving the SOLF problem. Quite a few solutions have been given for the SOLF problem [1], [11], [15], [17], [18], [25]. It is interesting to note that the SOLF related problems were originally studied in economic applications, where the number of variables is usually much bigger than the number of fractional terms. As a result, many previous SOLF algorithms were designed to target problems with only a few fractional terms (less than 10) for a reasonable
7149198
A fault-tolerant approach to secure information retrieval
Several private information retrieval (PIR) schemes were proposed to protect users' privacy when sensitive information stored in database servers is retrieved. However, existing PIR schemes assume that any attack to the servers does not change the information stored and any computational results. We present a novel fault-tolerant PIR scheme (called FT-PIR) that protects users' privacy and at the same time ensures service availability in the presence of malicious server faults. Our scheme neither relies on any unproven cryptographic assumptions nor the availability of tamper-proof hardware. A probabilistic verification function is introduced into the scheme to detect corrupted results. Unlike previous PIR research that attempted mainly to demonstrate the theoretical feasibility of PIR, we have actually implemented both a PIR scheme and our FT-PIR scheme in a distributed database environment. The experimental and analytical results show that only modest performance overhead is introduced by FT-PIR while comparing with PIR in the fault-free cases. The FT-PIR scheme tolerates a variety of server faults effectively. In certain fail-stop fault scenarios, FT-PIR performs even better than PIR. It was observed that 35.82% less processing time was actually needed for FT-PIR to tolerate one server fault.
17341019
Automatically detecting criminal identity deception: an adaptive detection algorithm
Identity deception, specifically identity concealment, is a serious problem encountered in the law enforcement and intelligence communities. In this paper, the authors discuss techniques that can automatically detect identity deception. Most of the existing techniques are experimental and cannot be easily applied to real applications because of problems such as missing values and large data size. The authors propose an adaptive detection algorithm that adapts well to incomplete identities with missing values and to large datasets containing millions of records. The authors describe three experiments to show that the algorithm is significantly more efficient than the existing record comparison algorithm with little loss in accuracy. It can identify deception having incomplete identities with high precision. In addition, it demonstrates excellent efficiency and scalability for large databases. A case study conducted in another law enforcement agency shows that the authors' algorithm is useful in detecting both intentional deception and unintentional data errors
8376312
Transparent runtime randomization for security
A large class of security attacks exploit software implementation vulnerabilities such as unchecked buffers. This paper proposes transparent runtime randomization (TRR), a generalized approach for protecting against a wide range of security attacks. TRR dynamically and randomly relocates a program's stack, heap, shared libraries, and parts of its runtime control data structures inside the application memory address space. Making a program's memory layout different each time it runs foils the attacker's assumptions about the memory layout of the vulnerable program and makes the determination of critical address values difficult if not impossible. TRR is implemented by changing the Linux dynamic program loader, hence it is transparent to applications. We demonstrate that TRR is effective in defeating real security attacks, including malloc-based heap overflow, integer overflow, and double-free attacks, for which effective prevention mechanisms are yet to emerge. Furthermore, TRR incurs less than 9% program startup overhead and no runtime overhead.