18640612
On approximating minimum vertex cover for graphs with perfect matching
It has been a challenging open problem whether there is a polynomial time approximation algorithm for the VERTEX COVER problem whose approximation ratio is bounded by a constant less than 2. In this paper, we study the VERTEX COVER problem on graphs with perfect matching (shortly, VC-PM). We show that if the VC-PM problem has a polynomial time approximation algorithm with approximation ratio bounded by a constant less than 2, then so does the VERTEX COVER problem on general graphs. Approximation algorithms for VC-PM are developed, which induce improvements over previously known algorithms on sparse graphs. For example, for graphs of average degree 5, the approximation ratio of our algorithm is 1.414, compared with the previously best ratio 1.615 by Halldorsson and Radhakrishnan.
5242879
Interactive rind modeling
In this paper, we describe a technique, with roots in topological graph theory, that we call rind modeling. It provides for the easy creation of surfaces resembling peeled and punctured rinds. We show how the method's two main steps of: 1) creation of a shell or crust like the rind of an orange, and 2) opening holes in the crust by punching or peeling can be encapsulated into a real time semi-automatic interactive algorithm. We include a number of worked examples, some by students in a first modeling course, that demonstrate the ease with which a large variety of intricate rind shapes can be created.
16331940
Optimal Parallel Routing in Star Networks
Star networks have recently been proposed as attractive alternatives to the popular hypercube for interconnecting processors on a parallel computer. In this paper, we present an efficient algorithm that constructs an optimal parallel routing in star networks. Our result improves previous results for the problem.
31382426
Strong Fault-Tolerance: Parallel Routing in Networks with Faults
A d-regular network G is strongly fault-tolerant if for any copy Gf of G with at most d - 2 faulty nodes, every pair of nonfaulty nodes u and v in Gf admits min{df(u), df (v)} node-disjoint paths in Gf from u to v, where df(u) and df(v) are the degrees of the nodes u and v in Gf. We show that popular network structures, such as hypercube and star networks, are strongly fault-tolerant. We develop efficient algorithms that construct the maximum number of node-disjoint paths of optimal or nearly optimal length in these networks with faulty nodes. Our algorithms are optimal in terms of their running time.
2261180
Graph Ear Decompositions and Graph Embeddings
Ear decomposition of a graph has been extensively studied in relation to graph connectivity. In this paper, a connection of ear decomposition to graph embeddings is exhibited. It is shown that constructing a maximum-paired ear decomposition of a graph and constructing a maximum-genus embedding of the graph are polynomial-time equivalent. Applications of this connection are discussed.
1021255
A minimal and complete set of operators for the development of robust manifold mesh modelers
In this paper, we identify a minimal and complete set of fundamental operators, which is necessary and sufficient for performing all homeomorphic and topological operations on 2- manifold mesh structures. Efficient algorithms are developed for the implementation of these operators. We also developed a set of powerful, user-friendly, and effective operators at the level of user-interface. Using these operators, we have developed a prototype system for robust, interactive, and user-friendly modeling of orientable 2-manifold meshes. Users of our system can perform a large set of homeomorphic and topological changes with these user-interface level operators. Our system is topologically robust in the sense that users will never create invalid 2-manifold mesh structure with these operators. In our system, the homeomorphic and topological surgery operations can be applied alternatively on 2-manifold meshes. With our system, users can blend surfaces, construct rinds, and open holes on these rind shapes. With our system, the shapes that look like solid, non-manifold, or 2-manifold with boundary can be manipulated. The system also provides automatic texture mapping during topology changes.
2913360
Dynamic verification of temporal constraints on-the-fly for workflow systems
Temporal verification is an important method to check the temporal correctness of workflow management systems (WfMSs). However, the current temporal verification is relatively independent of the workflow system environments. It does not pay sufficient attention to the interrelationship between the temporal verification at different stages, the mutual dependency between some temporal constraints, and the run-time checkpoint selection strategy, which hence hinders the incorporation and consistency between the temporal verification and the workflow system environments. In this paper, we effectively integrate the temporal verification at different stages and explore the dependency between some temporal constraints. In addition, we present a new effective runtime checkpoint selection strategy which dynamically selects appropriate checkpoints based on the activity completion duration. Furthermore, based on these analyses, we develop some new methods for more efficient temporal verification. These analyses and new methods help to eliminate the gap between the temporal verification and the workflow system environments.
36905463
Quasi-threshold Graphs
Abstract Quasi-threshold graphs are defined recursively by the following rules: 1. (1) K1 is a quasi-threshold graph, 2. (2) adding a new vertex adjacent to all vertices of a quasi-threshold graph results in a quasi-threshold graph, 3. (3) the disjoint union of two quasi-threshold graphs is a quasi-threshold graph. This paper gives some new equivalent definitions of a quasi-threshold graph. From them, linear time recognition algorithms follow. We also give linear time algorithms for the edge domination problem and the bandwidth problem in this class of graphs.
6316461
Partitioned optimization algorithms for multiple sequence alignment
Multiple sequence alignment is an important and difficult problem in molecular biology and bioinformatics. In this paper, we propose a partitioning approach that significantly improves the solution time and quality by utilizing the locality structure of the problem. The algorithm solves the multiple sequence alignment in three stages. First, an automated and suboptimal partitioning strategy is used to divide the set of sequences into several subsections. Then a multiple sequence alignment algorithm based on ant colony optimization is used to align the sequences of each subsection. Finally, the alignment of original sequences can be obtained by assembling the result of each subsection. The ant colony algorithm is highly optimized in order to avoid local optimal traps and converge to global optimal efficiently. Experimental results show that the algorithm can significantly reduce the running time and improve the solution quality on large-scale multiple sequence alignment benchmarks.
5642826
A garbage-collecting typed assembly language
Typed assembly languages usually support heap allocation safely, but often rely on an external garbage collector to deallocate objects from the heap and prevent unsafe dangling pointers. Even if the external garbage collector is provably correct, verifying the safety of the interaction between TAL programs and garbage collection is nontrivial. This paper introduces a typed assembly language whose type system is expressive enough to type-check a Cheney-queue copying garbage collector, so that ordinary programs and garbage collection can co-exist and interact inside a single typed language. The only built-in types for memory are linear types describing individual memory words, so that TAL programmers can define their own object layouts, method table layouts, heap layouts, and memory management techniques.
6192242
Computing Maximum-Scoring Segments in Almost Linear Time
Given a sequence, the problem studied in this paper is to find a set of k disjoint continuous subsequences such that the total sum of all elements in the set is maximized. This problem arises naturally in the analysis of DNA sequences. The previous best known algorithm requires Θ(n log n) time in the worst case. For a given sequence of length n, we present an almost linear-time algorithm for this problem. Our algorithm uses a disjoint-set data structure and requires O(nα(n, n)) time in the worst case, where α(n, n) is the inverse Ackermann function.