31564513
Packing of Unequal Spheres and Automated Radiosurgical Treatment Planning
We study an optimization problem of packing unequal spheres into a three-dimensional (3D) bounded region in connection with radiosurgical treatment planning. Given an input (R, V, S, L), where R is a 3D bounded region, V a positive integer, S a multiset of spheres, and L a location constraint on spheres, we want to find a packing of R using the minimum number of spheres in S such that the covered volume is at least V; the location constraint L is satisfied; and the number of points on the boundary of R that are touched by spheres is maximized. Such a packing arrangement corresponds to an optimal radiosurgical treatment planning. Finding an optimal solution to the problem, however, is computationally intractable. In particular, we show that this optimization problem and several related problems are NP-hard. Hence, some form of approximations is needed. One approach is to consider a simplified problem under the assumption that spheres of arbitrary (integral) diameters are available with unlimited supply, and there are no location constraints. This approach has met with certain success in medical applications using a dynamic programming algorithm (Bourland and Wu, 1996; Wu, 1996). We propose in this paper an improvement to the algorithm that can greatly reduce its computation cost.
17726002
Average-case completeness of a word problem for groups
This paper presents a bounded word problem for groups whose random instances are hard on average. The problem is to decide, when given a finitely presented group G, words ~, y, z, and an integer k, whether (Z–lyZ)Z can be obtained from Z(x–l yz) in G using elementary Tietze transformations for at most k times. We show that the problem is average-case NP-complete when instances are chosen at random under a uniform distribution. NP-completeness of more general bounded word problems for groups is shown as well.
32837558
On average P vs. average NP
Structures of polynomial-time computable distributions and polynomial-time many-one reductions on randomized decision problems are investigated. The scope is widened from the most studied class DNP (distributional-NP) to the class ANP (average-NP), which consists of randomized decision problems accepted by nondeterministic Turing machines in average polynomial time. Results indicate that the structures of average-case complexity classes are very different from their counterparts in worst-case complexity due to the complex structures of probability distributions and distribution functions.<<ETX>>
7902129
Efficient Minimization of Numerical Summation Errors
Given a multiset X={x 1,... x n } of real numbers, the floating-point set summation (FPS) problem asks for S n = x 1+...+ x n , and the floating point prefix set summation problem (FPPS) asks for S k =x 1+...+x k for all k = 1, ... n. Let E k * denote the minimum worst-case error over all possible orderings of evaluating S k . We prove that if X has both positive and negative numbers, it is NP-hard to compute S n with the worst-case error equal to E n * . We then give the first known polynomial-time approximation algorithm for computing Sn that has a provably small error for arbitrary X. Our algorithm incurs a worstcase error at most 2([log(n−1)]+1) E n * . After X is sorted, it runs in O(n) time, yielding an O(n 2)-time approximation algorithm for computing S k for all k = 1, ..., n such that the worst-case error for each S k is less than 2(⌈ log(k−1)⌋+ 1)E k * .
206565969
Immunity of Complete Problems
Abstract Two necessary and sufficient conditions for all E -complete sets to contain dense P subsets are shown. We then prove that every ≤ p m -hard for E set and its complement contain dense E ∩UP subsets. As a corollary, every NE -complete set and its complement contain dense E ∩UP subsets.
15313247
Performance of a MAC protocol for WDM networks with on-line scheduling
This paper investigates the performance of media access protocols based on on-line scheduling for an optically connected star-coupled system with wavelength division multiple access channels. Hybrid access protocols combining reservation and pre-allocation of receiver channels have been previously proposed. Transmission consisted of a reservation phase followed by a data phase. Each node was allowed to place a reservation for one WDM channel. This protocol is extended in this paper by allowing reservations on multiple channels and using simple on-line scheduling algorithms. Existing scheduling algorithms (all are off-line) for similar reservation problems tend to have high implementation and computational complexity. We require that scheduling algorithms be real-time and amenable to hardware implementation. The performance of the extended protocol incorporating two simple on-line scheduling algorithms is presented in this paper. We show that the slight increased computational overhead with scheduling is justified by reduced packet latency and higher utilization, especially for client-server traffic.
11808205
Mending broken handwriting with a macrostructure analysis method to improve recognition
Abstract Broken characters always create problems in handwriting recognition systems, especially those using boundary and/or skeleton information. This paper presents a macrostructure analysis (MSA) mending method based on skeleton and boundary information and an MSA that investigates the stroke tending direction and other properties of handwritings. A new skeleton end extension algorithm is introduced, which compensates the defectiveness of the skeletonization algorithm and obtains a satisfactory skeleton. When combined with suitable parameters, improved performance from a handwriting classifier is achieved. The experimental results from over 13 000 numerals show the efficiency and robustness of the proposed method, raising recognition rates by over 10% for broken handwritten digits, from 74.8% to 86.4%.
21513395
VLSI architecture and implementation for FS1016 CELP decoder with reduced power and memory requirements
Abstract The code-excited linear predictive (CELP) coder is the most effective technique among various linear predictive coding methods for speech compression. Hence, designing a relatively low-cost and low-power CELP decoder chip for the portable systems and wireless digital communication environment becomes increasingly important. This paper presents the VLSI architecture and chip implementation for the FS1016 CELP decoder with reduced power and memory requirements. A single-chip implementation of the CELP decoder drastically reduces the cost and the size of many CELP vocoder systems. The decoder chip can achieve the following: (1) excellent accuracy results due to the accuracy studies for the finite word length, (2) power savings and high-speed operations owing to the combined advantages of pipeline and concurrent processing structures, (3) table size reducing by applying the memoryless realization for stochastic codebook and partial sums technique and (4) specification satisfying the FS1016 CELP coder. Fabricated with 0.8 μm double-metal CMOS technology, the chip contains approximately 13 000 transistors occupying a 6.1 × 6.2 mm2 area. It has been tested to be fully functional at IMS XL-60 tester and is the first working FS1016 CELP 4.8 K decoder chip. In particular, the fixed-point accuracy studies for the CELP decoder are also addressed herein.
206566936
Approximate Tree Matching in the Presence of Variable Length Don't Cares
Ordered labeled trees are trees in which the sibling order matters. This paper presents algorithms for three problems having to do with approximate matching for such trees with variable length don′t cares (VLDCs). In strings, a VLDC symbol in the pattern may substitute for zero or more symbols in the data string. For example, if "com∗er" is the pattern, then the "∗" would substitute for the substring "put" when matching the data string "computer." Approximate VLDC matching in strings means that after the best possible substitution, the pattern still need not be the same as the data string for a match to be allowed. For example, "com∗er" matches "counter" within distance one (representing the cost of removing the "m" from "com∗er" and having the "∗" substitute for "unt"). We generalize approximate VLDC string matching to three algorithms for approximate VLDC matching on trees. The time complexity of our algorithms is O(|P| × |D| × min(depth(P), leaves(P)) × min(depth(D), leaves(D))) (where |P| and |D| are the number of nodes respectively of the pattern P and the data tree D), the same as for the best approximate tree matching algorithm without VLDCs previously reported.
13574031
Mining genes in DNA using GeneScout
In this paper we present a new system, called GeneScout, for predicting gene structures in vertebrate genomic DNA. The system contains specially designed hidden Markov models (HMMs) for detecting functional sites including protein-translation start sites, mRNA splicing junction donor and acceptor sites, etc. Our main hypothesis is that, given a vertebrate genomic DNA sequence S, it is always possible to construct a directed acyclic graph G such that the path for the actual coding region of S is in the set of all paths on G. Thus, the gene detection problem is reduced to that of analyzing the paths in the graph G. A dynamic programming algorithm is used to find the optimal path in G. The proposed system is trained using an expectation-maximization (EM) algorithm and its performance on vertebrate gene prediction is evaluated using the 10-way cross-validation method. Experimental results show the good performance of the proposed system and its complementarity to a widely used gene detection system.
16538539
Optimal jumper insertion for antenna avoidance under ratio upper-bound
Antenna effect may damage gate oxides during plasma-based fabrication process. The antenna ratio of total exposed antenna area to total gate oxide area is directly related to the amount of damage. Jumper insertion is a common technique applied at routing and post-layout stages to avoid and to fix the problems caused by the antenna effect. This paper presents an optimal algorithm for jumper insertion under the ratio upper-bound. It handles Steiner trees with obstacles. The algorithm us based on dynamic programming while works on free trees. The time complexity is O(alpha|V|2 ) and the space complexity is O(|V|2), where |V| is the number of nodes in the routing tree and a is a factor depending on how to find a non-blocked position on a wire for a jumper