33534823
Improved Approximation Algorithms for Maximum Resource Bin Packing and Lazy Bin Covering Problems
In this paper, we study two variants of the bin packing /covering problems called Maximum Resource Bin Packing (MRBP) and Lazy Bin Covering (LBC) problems, and present new approximation algorithms for each of them. For the offline MRBP problem, the previous best known approximation ratio is $\frac{6}{5}=1.2$, achieved by the classical First-Fit-Increasing (FFI) algorithm [1]. In this paper, we give a new FFI-type algorithm with an approximation ratio of $\frac{80}{71}\approx 1.12676$. For the offline LBC problem, it has been shown in [2] that the classical First-Fit-Decreasing (FFD) algorithm achieves an approximation ratio of $\frac{71}{60}\approx 1.18333$. In this paper, we present a new FFD-type algorithm with an approximation ratio of $\frac{17}{15}\approx 1.13333$. Both algorithms are simple, run in near linear time (i.e., O(n logn)), and therefore are practical.
29728094
Graph Bandwidth of Weighted Caterpillars
Graph bandwidth minimization (GBM) is a classical and challenging problem in graph algorithms and combinatorial optimization. Most of existing researches on this problem have focused on unweighted graphs. In this paper, we study the bandwidth minimization problem of weighted caterpillars, and propose several algorithms for solving various types of caterpillars and general graphs. More specifically, we show that the GBM problem on caterpillars with hair-length at most 2 and the GBM problem on star-shape caterpillars are NP-complete, and give a lower bound of the graph bandwidth for general weighted graphs. For caterpillars with hair-length at most 1, we present an O(n log n log(nwmax))-time algorithm to compute an optimal bandwidth layout, where n is the total number of vertices in the graph and wmax is the maximum wedge weight. For caterpillars with hair-length at most k, we give a k-approximation algorithm. For arbitrary caterpillars and general graphs, we give a heuristic algorithm and some experimental results. Experiments show that the solutions obtained by our heuristic algorithm are roughly within a factor of c log(n) of the lower bound for a small number c, which is consistent with the inapproximability results of this problem (i.e., no constant approximation for the GBM problem unless P = NP). © 2006 Published by Elsevier B.V.
6260724
Finding an optimal path without growing the tree
For problems on computing an optimal path as well as its length in a certain setting, the "standard" approach for finding an actual optimal path is by building (or "growing") a single-source optimal path tree. In this paper, we study a class of optimal path problems with the following phenomenon: The space complexity of the algorithms for reporting the lengths of single-source optimal paths for these problems is asymptotically smaller than the space complexity of the "standard" tree-growing algorithms for finding actual optimal paths. We present a general and efficient algorithmic paradigm for finding an actual optimal path for such problems without having to grow a single-source optimal path tree. Our paradigm is based on the "marriage-before-conquer" strategy, the prune-and-search technique, and a new data structure called clipped trees. The paradigm enables us to compute an actual path for a number of optimal path problems and dynamic programming problems in computational geometry, graph theory, and combinatorial optimization. Our algorithmic solutions improve the space bounds (in certain cases, the time bounds as well) of the previously best known algorithms, and settle some open problems. Our techniques are likely to be applicable to other problems.
21098955
Topological Peeling and Implementation
We present a new approach, called topological peeling, and its implementation for traversing a portion AR of the arrangement formed by n lines within a convex region R on the plane. Topological peeling visits the cells of AR in a fashion of propagating a "wave" of a special shape (called a double-wriggle curve) starting at a single source point. This special traversal fashion enables us to solve several problems (e.g., computing shortest paths) on planar arrangements to which previously best known arrangement traversal techniques such as topological sweep and topological walkm ay not be directly applicable. Our topological peeling algorithm takes O(K + n log(n + r)) time and O(n + r) space, where K is the number of cells in AR and r is the number of boundary vertices of R. Comparing with topological walk, topological peeling uses a simpler and more efficient way to sweep different types of lines, and relies heavily on exploring small local structures, rather than a much larger global structure. Experiments show that, on average, topological peeling outperforms topological walkb y 10 - 15% in execution time.
28240465
Motion Tracking and Intensity Surface Recovery in Microscopic Nuclear Images
Current techniques for microscopic imaging do not provide necessary spatial and temporal resolutions for real time visualization of the nucleus. Images can only be acquired in time lapse mode, leading to significant loss of information between image frames. Such data, if available, can be extremely helpful in the study of nuclear organization and function. In this paper, we present a gamut of geometric-technique-based approaches for solving the problem. Our techniques, working together, can effectively recover complicated motion and deformation as well as the change of intensity surfaces from pairs of images in a microscopic image sequence, and has low time complexity, particularly desirable by many biological applications where large amount of DNA need to be processed. These techniques are also readily applicable to other types of images for reconstructing motion and intensity surfaces of deformable objects.
14297439
Geometric permutations of high dimensional spheres
We prove the maximum number of geometric permutations, induced by line transversals to a set of <i>n</i> pairwise disjoint congruent spheres in <i>R<sup>d</sup></i> with <i>d</i> ⪈ 3, is no more than 4 when <i>n</i> is sufficiently large, achieving the best known upper bound for this problem. We also prove the maximum number of geometric permutations of a set of <i>n</i> noncongruent spheres of bounded radius ratio in R<sup>d</sup>, <i>d</i> ⪈ 3, is at most 2<sup>[√2<i>M</i>]+1</sup>, where <i>M</i> is the ratio or the largest radius and the smallest radius. Our result settles a conjecture in combinatorial geometry.
8575653
Using Shortest Path Algorithms to Identify Criminal Associations
Frequently in criminal investigations, law enforcement agencies face the problem of identifying associations between a group of entities such as individuals and organizations. In this paper we present a link analysis technique to solve such a problem. This approach uses shortest path algorithms to find the strongest associations between two or more given entities. The experimental results have demonstrated that our approach is potentially useful in terms of quality and efficiency. Specifically, we found that the two-tree Priority-First Search algorithm in most cases was the fastest algorithm to find shortest paths and the paths found consisted of meaningful criminal associations around 80 percent of the time.
2460253
Approximate processing of massive continuous quantile queries over high-speed data streams
Quantile computation has many applications including data mining and financial data analysis. It has been shown that an /spl epsi/-approximate summary can be maintained so that, given a quantile query (/spl phi/,/spl epsi/), the data item at rank /spl lceil//spl phi/N/spl rceil/ may be approximately obtained within the rank error precision /spl epsi/N over all N data items in a data stream or in a sliding window. However, scalable online processing of massive continuous quantile queries with different /spl phi/ and /spl epsi/ poses a new challenge because the summary is continuously updated with new arrivals of data items. In this paper, first we aim to dramatically reduce the number of distinct query results by grouping a set of different queries into a cluster so that they can be processed virtually as a single query while the precision requirements from users can be retained. Second, we aim to minimize the total query processing costs. Efficient algorithms are developed to minimize the total number of times for reprocessing clusters and to produce the minimum number of clusters, respectively. The techniques are extended to maintain near-optimal clustering when queries are registered and removed in an arbitrary fashion against whole data streams or sliding windows. In addition to theoretical analysis, our performance study indicates that the proposed techniques are indeed scalable with respect to the number of input queries as well as the number of items and the item arrival rate in a data stream.
11486473
Circumference of Graphs with Bounded Degree
Karger, Motwani, and Ramkumar Algorithmica, 18 (1997), pp. 82--98] have shown that there is no constant approximation algorithm to find a longest cycle in a Hamiltonian graph, and they conjectured that this is the case even for graphs with bounded degree. On the other hand, Feder, Motwani, and Subi [SIAM J. Comput., 31 (2002), pp. 1596--1607] have shown that there is a polynomial time algorithm for finding a cycle of length $n^{\log_32}$ in a 3-connected cubic n-vertex graph. In this paper, we show that if G is a 3-connected n-vertex graph with maximum degree at most d, then one can find, in O(n3) time, a cycle in G of length at least $\Omega(n^{\log_b2})$, where $b=2(d-1)^2+1$.
17686330
Protein Threading by Linear Programming
Protein three-dimensional structure prediction through threading approach has been extensively studied and various models and algorithms have been proposed. In order to further explore ways to improve accuracy and efficiency of the threading process, this paper investigates the effectiveness of a new method: protein threading via linear programming. Based on the contact map model of protein 3D structure, we formulate the protein threading problem as a large scale integer programming problem, then relax to a linear programming problem, and finally solve the integer program by a branch-and-bound method. The final solution is optimal with respect to energy functions incorporating pairwise interaction and allowing variable gaps. The algorithm has been implemented as software package RAPTOR--RApid Protein Threading predictOR. Experimental results for fold recognition show that RAPTOR significantly outperforms other programs at the fold similarity level. The RAPTOR webserver is at http://www.cs.uwaterloo.ca/-j3xu/RAPTOR_form.htm.
17196137
Fighting organized crimes: using shortest-path algorithms to identify associations in criminal networks
Effective and efficient link analysis techniques are needed to help law enforcement and intelligence agencies fight organized crimes such as narcotics violation, terrorism, and kidnapping. In this paper, we propose a link analysis technique that uses shortest-path algorithms, priority-first-search (PFS) and two-tree PFS, to identify the strongest association paths between entities in a criminal network. To evaluate effectiveness, we compared the PFS algorithms with crime investigators' typical association-search approach, as represented by a modified breadth-first-search (BFS). Our domain expert considered the association paths identified by PFS algorithms to be useful about 70% of the time, whereas the modified BFS algorithm's precision rates were only 30% for a kidnapping network and 16.7% for a narcotics network. Efficiency of the two-tree PFS was better for a small, dense kidnapping network, and the PFS was better for the large, sparse narcotics network.