9386148
Orthogonal factorizations of graphs
Let G be a graph with vertex set V(G) and edge set E(G), and let g and f be two nonnegative integer-valued functions defined on V(G) such that g(x) ≤ f(x) for every vertex x of V(G). We use dG(x) to denote the degree of a vertex x of G. A graph G is called a (g,f)-graph if g(x) ≤ dG(x) ≤ f(x) for each x ∈ V(G). Then a spanning subgraph F of G is said to be a (g,f)-factor of G if F itself is a (g,f)-graph. A (g,f)-factorization of G is a partition of E(G) into edge disjoint (g,f)-factors. Let F = {F1,F2,... ,Fm} be a factorization of G and H be a subgraph of G with m edges. If Fi, 1 ≤ i ≤ m, has exactly one edge in common with H, we say that F is orthogonal to H. In this paper it is proved that every (mg + k,mf - k)-graph contains a subgraph R such that R has a (g,f)-factorization orthogonal to a given subgraph with k edges, where m and k are positive integers with 1 ≤ k > m and g(x) ≥ 0. This result has been conjectured by Yan in Yan (Sci. China Ser. A 41(1) (1998) 48).
40174055
A PTAS for Distinguishing (Sub)string Selection
Consider two sets of strings, B (bad genes) and G (good genes), as well as two integers db and dg (db ? dg). A frequently occurring problem in computational biology (andother fields) is to finda (distinguishing) substring s of length L that distinguishes the bad strings from goodstrings, i.e., for each string si ? B there exists a length-L substring ti of si with d(s, ti) ? db (close to badstrings) andfor every substring ui of length L of every string gi ? G, d(s, ui) ? dg (far from goodstrings). We present a polynomial time approximation scheme to settle the problem, i.e., for any constant ? > 0, the algorithm finds a string s of length L such that for every si ? B, there is a length-L substring ti of si with d(ti, s) ? (1+?)db and for every substring ui of length L of every gi ? G, d(ui, s) ? (1 - ?)dg, if a solution to the original pair (db ? dg) exists.
7761968
A PTAS for Semiconductor Burn-in Scheduling
In this paper a polynomial time approximation scheme, PTAS for short, is presented for the problem of scheduling jobs in a batch processing system. Each job has a pre-defined release date, which indicates when the job is available, and a pre-defined burn-in time, which is the least time needed for processing the job. At one time, at most B jobs can be processed together, where B is a pre-given number. No preemption is permitted.
29830975
A PTAS for Minimizing Total Completion Time of Bounded Batch Scheduling
We consider a batch processing system {pi : i = 1, 2,…,n} where pi is the processing time of job i, and up to B jobs can be processed together such that the handling time of a batch is the longest processing time among jobs in the batch. The number of job types m is not fixed and all the jobs are released at the same time. Jobs are executed non-preemptively. Our objective is to assign jobs to batches and sequence the batches so as to minimize the total completion time. The best previously known result is a 2–approximation algorithm. In this paper, we establish the first polynomial time approximation scheme (PTAS) for the problem.
7451094
Orthogonal (g, f)-factorizations in networks
Let G = (V,E) be a graph and let g and f be two integer-valued functions defined on V such that k ≤ g(x) ≤ f(x) for all x ∈ V . Let H1,H2, · · · ,Hk be subgraphs of G such that |E(Hi)| = m, 1 ≤ i ≤ k, and V (Hi) ∩ V (Hj) = ∅ when i 6= j. In this paper it is proved that every (mg + m − 1,mf −m + 1)-graph G has a (g, f)-factorization orthogonal to Hi for i = 1, 2, · · · , k and shown that there are polynomial-time algorithms to find the desired (g, f)-factorizations.
9766004
A PTAS for Minimizing Total Completion Time of Bounded Batch Scheduling
We consider a batch processing system {pi : i = 1, 2,..., n} where pi is the processing time of job i, and up to B jobs can be processed together such that the handling time of a batch is the longest processing time among jobs in the batch. The number of job types m is not fixed and all the jobs are released at the same time. Jobs are executed nonpreemptively. Our objective is to assign jobs to batches and sequence the batches so as to minimize the total completion time. The best previously known result is a 2-approximation algorithm due to D. S. Hochbaum and D. Landy [6]. In this paper, we establish the first polynomial time approximation scheme (PTAS) for the problem.
43737883
Translation Initiation Sites Prediction with Mixture Gaussian Models
Translation initiation sites (TIS) are important signals in cDNA sequences. Many research efforts have tried to predict TIS in cDNA sequences. In this paper, we propose using mixture Gaussian models to predict TIS in cDNA sequences. Some new global measures are used to generate numerical features from cDNA sequences, such as the length of the open reading frame downstream from ATG, the number of other ATGs upstream and downstream from the current ATGs, etc. With these global features, the proposed method predicts TIS with sensitivity 98% and specificity 92%. The sensitivity is much better than that from other methods. We attribute the improvement in sensitivity to the nature of the global features and the mixture Gaussian models.
10744767
Typing Aberrance in Signal Transduction
We have developed a calculus, called Ipi, for describing the aberrance in biological models. Our approach extends the traditional pi calculus to handle aberrant process in the signal transduction. In this paper we propose a typing system that replaces the tag system of Ipi calculus. It is shown that the typing system is equal to the tag system in terms of the expressive power.
17312614
Secrecy of Signals by Typing in Signal Transduction
We discuss secrecy of signals in signal transduction. As we have developed a basic concurrent language with interferencial coefficients, Iπ-calculus, to describe aberrance in biological models, a typing system for Iπ-calculus is proposed for achieving secrecy of signals in signal transduction. We show that this typing system guarantees that, if signal transduction typechecks, then it does not leak aberrance of signals.
33634319
A genetic algorithm for the multiple destination routing problems
The multiple destination routing (MDR) problem can be formulated as finding a minimal cost tree which contains designated source and multiple destination nodes so that certain constraints in a given communication network are satisfied. This is a typical NP-hard problem, and therefore only heuristic algorithms are of practical value. As a first step, a new genetic algorithm is developed to solve the MDR problems without constraints. It is based on the transformation of the underlying network of an MDR problem into its distance complete form, a natural chromosome representation of a minimal spanning tree (an individual), and a completely new computation of the fitness of individual. Compared with the known genetic algorithms and heuristic algorithms for the same problem, the proposed algorithm has several advantages. First, it guarantees convergence to an optimal solution with probability one. Second, not only are the resultant solutions all feasible, the solution quality is also much higher than that obtained by the other methods (indeed, in almost every case in our simulations, the algorithm can find the optimal solution of the problem). Third, the algorithm is of low computational complexity, and this can be decreased dramatically as the number of destination nodes in the problem increases. The simulation studies for the sparse and dense networks all demonstrate that the proposed algorithm is highly robust and very efficient in the sense of yielding high-quality solutions.
2186483
Improvements for the Symbolic Verification of Timed Automata
Based on the equivalence relation for location based reachability between continuous and integer semantics of closed timed automata, Beyer et al. have implemented the verifier Rabbit, with the uniform representation of reachable configurations. However, the growth of maximal constant of clock variables will decline the performance of Rabbit. The paper proposes an improved symbolic method, using binary decision diagrams (BDDs) to store the symbolic representation of discretized states, for the verification of timed systems. Compared with Rabbit, experiments demonstrate that besides the memory reduction, our implementation is also less sensitive to the size of clock domain.