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ABSTRACT: Sequence alignment is a fundamental problem in computational biology, which is also important in theoretical computer science. In this paper, we consider the problem of aligning a set of sequences subject to a given constrained sequence. Given two sequences \(A=a_1a_2\ldots a_n\) and \(B=b_1b_2\ldots b_n\) with a given distance function and a constrained sequence \(C=c_1c_2\ldots c_k\), our goal is to find the optimal sequence alignment of A and B w.r.t. the constraint C. We investigate several variants of this problem. If \(C=c^k\), i.e., all characters in C are same, the optimal constrained pairwise sequence alignment can be solved in \(O(\min \{kn^2,(tk)n^2\})\) time, where t is the minimum number of occurrences of character c in A and B. If in the final alignment, the alignment score between any two consecutive constrained characters is upper bounded by some value, which is called GBCPSA, we give a dynamic programming with the time complexity \(O(kn^4/\log n)\). For the constrained centerstar sequence alignment (CCSA), we prove that it is NPhard to achieve the optimal alignment even over the binary alphabet. Furthermore, we show a negative result for CCSA, i.e., there is no polynomialtime algorithm to approximate the CCSA within any constant ratio. Journal of Combinatorial Optimization 01/2015; DOI:10.1007/s1087801599146 · 1.04 Impact Factor

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ABSTRACT: We consider the problem of aligning a set of sequences subject to a given constrained sequence, which has applications in computational biology. In this paper we show that sequence alignment for two sequences A and B with a given distance function and a constrained sequence of k identical characters (say character c) can be solved in O( min {kn
2,(t − k)n
2}) time, where n is the length of A and B, and t is the minimum number of occurrences of character c in A and B. We also prove that the problem of constrained centerstar sequence alignment (CCSA) is NPhard even over the binary alphabet. Furthermore, for some distance function, we show that no polynomialtime algorithm can approximate the CCSA within any constant ratio.

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ABSTRACT: An interesting problem in music information retrieval is to classify songs according to rhythms. A rhythm is represented by a sequence of “Quick” (Q) and “Slow” (S) symbols, which correspond to the (relative) duration of notes, such that S = 2Q. Christodoulakis et al. presented an efficient algorithm that can be used to classify musical sequences according to rhythms. In this article, the above algorithm is implemented, along with a naive brute force algorithm to solve the same problem. The theoretical time complexity bounds are analyzed with the actual running times achieved by the experiments, and the results of the two algorithms are compared. Furthermore, new efficient algorithms are presented that take temporal errors into account. This, the approximate pattern matching version, could not be handled by the algorithms previously presented. The running times of two algorithmic variants are analyzed and compared and examples of their implementation are shown. International Journal on Digital Libraries 08/2012; 12(23). DOI:10.1007/s0079901200850

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ABSTRACT: Wireless communication networks based on frequency division multiplexing (FDM in short) play an important role in the field of communications, in which each request can be satisfied by assigning a frequency. To avoid interference, each assigned frequency must be different from the neighboring assigned frequencies. Since frequencies are scarce resources, the main problem in wireless networks is how to fully utilize the given bandwidth of frequencies. In this paper, we consider the online call control problem. Given a fixed bandwidth of frequencies and a sequence of communication requests arriving over time, each request must be either satisfied immediately after its arrival by assigning an available frequency, or rejected. The objective of the call control problem is to maximize the number of accepted requests. We study the asymptotic performance of this problem, i.e., the number of requests in the sequence and the bandwidth of frequencies are very large. In this paper, we give a 7/3competitive algorithm, say CACO, for the call control problem in cellular networks, improving the previous 2.5competitive result, and show that CACO is best possible among a class of HYBRID algorithms. Information Processing Letters 01/2012; 112(12):2125. DOI:10.1016/j.ipl.2011.10.005 · 0.48 Impact Factor

Source Available from: psu.edu
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ABSTRACT: Given a complete binary tree of heighth, the online tree node assignment problem is to serve a sequence of assignment/release requests, where an assignment request, with an integer parameter0≤i≤h, is served by assigning a (tree) node of level (or height)i and a release request is served by releasing a specified assigned node. The node assignments have to guarantee that no node is assigned to two
assignment requests unreleased, and every leaftoroot path of the tree contains at most one assigned node. With assigned
node reassignments allowed, the target of the problem is to minimize the number of assignments/reassignments, i.e., the cost,
to serve the whole sequence of requests. This online tree node assignment problem is fundamental to many applications, including
OVSF code assignment in WCDMA networks, buddy memory allocation and hypercube subcube allocation.
Most of the previous results focus on how to achieve good performance when the same amount of resource is given to both the
online and the optimal offline algorithms, i.e., one tree. In this paper, we focus on resource augmentation, where the online
algorithm is allowed to use more trees than the optimal offline algorithm. By using different approaches, we give (1) a 1competitive
online algorithm, which uses (h+1)/2 trees and is optimal because (h+1)/2 trees are required by any online algorithm to match the cost of the optimal offline algorithm with one tree; (2) a 2competitive
algorithm with 3h/8+2 trees; (3) an amortized 8/3competitive algorithm with 11/4 trees; (4) a general amortized (4/3+α)competitive algorithm with (11/4+4/(3α)) trees, for 0<α≤4/3.
KeywordsOnline algorithms–Tree node assignment–Resource augmentation Journal of Combinatorial Optimization 10/2011; 22(3):359377. DOI:10.1007/s108780109292z · 1.04 Impact Factor

Source Available from: Xin Han
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ABSTRACT: Wireless Communication Networks based on Frequency Division Multiplexing (FDM in short) plays an important role in the field of communications, in which each request can be satisfied by assigning a frequency. To avoid interference, each assigned frequency must be different to the neighboring assigned frequencies. Since frequency is a scarce resource, the main problem in wireless networks is how to fully utilize the given bandwidth of frequencies. In this paper, we consider the online call control problem. Given a fixed bandwidth of frequencies and a sequence of communication requests arrive over time, each request must be either satisfied immediately after its arrival by assigning an available frequency, or rejected. The objective of call control problem is to maximize the number of accepted requests. We study the asymptotic performance of this problem, i.e., the number of requests in the sequence and the bandwidth of frequencies are very large. In this paper, we give a 7/3competitive algorithm for call control problem in cellular network, improving the previous 2.5competitive result. Moreover, we investigate the trianglefree cellular network, propose a 9/4competitive algorithm and prove that the lower bound of competitive ratio is at least 5/3. Comment: 12 pages, 4 figures

Source Available from: Deshi Ye
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ABSTRACT: Given a cellular (mobile telephone) network, whose geographical coverage area is divided into hexagonal cells, phone calls are serviced by assigning frequencies to them so that no two calls emanating from the same or neighboring cells are assigned the same frequency. Assuming an online arrival of calls, the goal is to minimize the span of frequencies used to serve all of the calls. By flrst considering ´colorable networks, which is a generalization of the (3colorable) cellular networks, we present a (´ + 1)=2competitive online algorithm. This algorithm, when applied to cellular networks, is efiectively a positive solution to the open problem posed in (3): Does a 2competitive online algorithm exist for frequency allocation in cellular networks? We further prove a matching lower bound, which shows that our 2competitive algorithm is optimal. We discover that an interesting phenomenon occurs for the online frequency allocation problem when the number of calls considered becomes large: previouslyderived optimal bounds on competitive ratios no longer hold true. For cellular networks, we show a new asymptotic lower and upper bounds of 1:5 and 1:9126, respectively, which breaks through the optimal bound of 2 shown above. Algorithmica 01/2010; 58(2):498515. DOI:10.1007/s0045300992792 · 0.57 Impact Factor

Source Available from: LapKei Lee
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ABSTRACT: This article extends the study of online algorithms for energyefficient deadline scheduling to the overloaded setting. Specifically, we consider a processor that can vary its speed between 0 and a maximum speed T to minimize its energy usage (the rate is believed to be a cubic function of the speed). As the speed is upper bounded, the processor may be overloaded with jobs and no scheduling algorithms can guarantee to meet the deadlines of all jobs. An optimal schedule is expected to maximize the throughput, and furthermore, its energy usage should be the smallest among all schedules that achieve the maximum throughput. In designing a scheduling algorithm, one has to face the dilemma of selecting more jobs and being conservative in energy usage. If we ignore energy usage, the best possible online algorithm is 4competitive on throughput [Koren and Shasha 1995]. On the other hand, existing work on energyefficient scheduling focuses on a setting where the processor speed is unbounded and the concern is on minimizing the energy to complete all jobs; O(1)competitive online algorithms with respect to energy usage have been known [Yao et al. 1995; Bansal et al. 2007a; Li et al. 2006]. This article presents the first online algorithm for the more realistic setting where processor speed is bounded and the system may be overloaded; the algorithm is O(1)competitive on both throughput and energy usage. If the maximum speed of the online scheduler is relaxed slightly to (1+&epsis;)T for some &epsis; > 0, we can improve the competitive ratio on throughput to arbitrarily close to one, while maintaining O(1)competitiveness on energy usage. ACM Transactions on Algorithms 12/2009; 6(1):10. DOI:10.1145/1644015.1644025 · 0.40 Impact Factor

Source Available from: citeseerx.ist.psu.edu
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ABSTRACT: Given a complete binary tree of heighth, the online tree node assignment problem is to serve a sequence of assignment/release requests, where an assignment request, with an integer parameter0 ≤ i ≤ h, is served by assigning a (tree) node at level (or height)i and a release request is served by releasing a specified assigned node. The node assignments have to guarantee that no node is assigned to two
assignment requests unreleased, and every leaftoroot path of the tree contains at most one assigned node. With assigned
node reassignments allowed, the target of the problem is to minimize the number of assignments/reassigments, i.e., the cost,
to serve the whole sequence of requests. This online tree node assignment problem is fundamental to many applications, including
OVSF code assignment in WCDMA networks, buddy memory allocation and hypercube subcube allocation.
Most of the previous results focus on how to achieve good performance when the same amount of resource is given to both the
online and the optimal offline algorithms, i.e., one tree. In this paper, we focus on resource augmentation, where the online
algorithm is allowed to use more trees than the optimal offline algorithm. By using different approaches, we give (1) a 1competitive
online algorithm, which uses (h + 1)/2 trees, and is optimal because (h + 1)/2 trees are required by any online algorithm to match the cost of the optimal offline algorithm with one tree; (2) a
2competitive algorithm with 3h/8 + 2 trees; (3) an amortized (4/3 + α)competitive algorithm with (11/4 + 4/(3α)) trees, for any α where 0 < α ≤ 4/3. 11/2009: pages 358367;

Source Available from: Prudence W. H. Wong
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ABSTRACT: We study the dynamic bin packing problem introduced by Coffman, Garey and Johnson. This problem is a generalization of the
bin packing problem in which items may arrive and depart from the packing dynamically. The main result in this paper is a
lower bound of 2.5 on the achievable competitive ratio, improving the best known 2.428 lower bound, and revealing that packing
items of restricted form like unit fractions (i.e., of size 1/k for some integer k), for which a 2.4985competitive algorithm is known, is indeed easier.
We also investigate the resource augmentation version of the problem where the online algorithm can use bins of size b (>1) times that of the optimal offline algorithm. An interesting result is that we prove b=2 is both necessary and sufficient for the online algorithm to match the performance of the optimal offline algorithm,
i.e., achieve 1competitiveness. Further analysis gives a tradeoff between the bin size multiplier 1b≤2 and the achievable competitive ratio. Algorithmica 01/2009; 53(2):172206. DOI:10.1007/s004530089185z · 0.57 Impact Factor

Source Available from: Prudence W. H. Wong
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ABSTRACT: Abstract This paper studies the dynamic bin packing problem, in which items arrive and depart at arbitrary time. We want to pack a sequence of unit fractions items (i.e., items with sizes 1=w for some integer w ‚ 1) into unitsize bins such that the maximum,number of bins ever used over all time is minimized. Tight and almost tight performance bounds are found for the family of anyflt algorithms, including flrstflt, bestflt, and worstflt. In particular, we show that the competitive ratio of bestflt and worstflt is 3, which is tight, and the competitive ratio of flrstflt lies between 2:45 and 2:4942. We also show that no online algorithm is better than 2:428competitive. Theoretical Computer Science 12/2008; 409(3):521529. DOI:10.1016/j.tcs.2008.09.028 · 0.52 Impact Factor

Source Available from: citeseerx.ist.psu.edu
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ABSTRACT: A con∞ictfree coloring for a given set of disks is a coloring of the disks such that for any point p on the plane there is a disk among the disks covering p having a color difierent from that of the rest of the disks that covers p. In the dynamic o†ine setting, a sequence of disks is given, we have to color the disks onebyone according to the order of the sequence and maintain the con∞ictfree property at any time for the disks that are colored. This paper focuses on unit disks, i.e., disks with radius one. We give an algorithm that colors a sequence of n unit disks in the dynamic o†ine setting using O(logn) colors. The algorithm is asymptotically optimal because ›(logn) colors is necessary to color some set of n unit disks for any value of n (9). Approximation and Online Algorithms, 6th International Workshop, WAOA 2008, Karlsruhe, Germany, September 1819, 2008. Revised Papers; 01/2008

Source Available from: Deshi Ye
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ABSTRACT: The online frequency allocation problem for cellular networks has been well studied in these years. Given a mobile telephone network, whose geographical coverage area is divided into cells, phone calls are served by assigning frequencies to them, and no two calls emanating from the same or neighboring cells are assigned the same frequency. Assuming an online setting that the calls arrive one by one, the problem is to minimize the span of the frequencies used. In this paper, we study the greedy approach for the online frequency allocation prob lem, which assigns the minimal available frequency to a new call so that the call does not interfere with calls of the same cell or neighboring cells. If the calls have inflnite duration, the competitive ratio of greedy algorithm has a tight upper bound of 17/7, which closes the gap of (17=7;2:5) in (3). If the calls have flnite duration, i.e., each call may be terminated at some time, the competitive ratio of the greedy algorithm has a tight upper bound of 3. Information Processing Letters 04/2007; 102:5561. DOI:10.1016/j.ipl.2006.11.015 · 0.48 Impact Factor

Source Available from: Prudence W. H. Wong
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ABSTRACT: Existing work on scheduling with energy concern has focused on minimizing the energy for completing all jobs or achieving
maximum throughput [19,2,7,13,14]. That is, energy usage is a secondary concern when compared to throughput and the schedules
targeted may be very poor in energy efficiency. In this paper, we attempt to put energy efficiency as the primary concern
and study how to maximize throughput subject to a userdefined threshold of energy efficiency. We first show that all deterministic
online algorithms have a competitive ratio at least Δ, where Δ is the maxmin ratio of job size. Nevertheless, allowing the online algorithm to have a slightly poorer energy efficiency
leads to constant (i.e., independent of Δ) competitive online algorithm. On the other hand, using randomization, we can reduce the competitive ratio to O(logΔ) without relaxing the efficiency threshold. Finally we consider a special case where no jobs are “demanding” and give a deterministic
online algorithm with constant competitive ratio for this case. Theory and Applications of Models of Computation, 4th International Conference, TAMC 2007, Shanghai, China, May 2225, 2007, Proceedings; 01/2007

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ABSTRACT: z ABSTRACT Given a mobile telephone network, whose geographical cov erage area is divided into cells, phone calls are serviced by assigning frequencies to them, so that no two calls emanat ing from the same or neighboring cells are assigned the same frequency. Assuming an online arrival of calls and the calls will not terminate, the problem is to minimize the span of frequencies used. By first considering ´colorable networks, which is a gen eralization of (the 3colorable) cellular networks, we present a (´ + 1)=2competitive online algorithm. This algorithm, when applied to cellular networks, is eectively SPAA 2007: Proceedings of the 19th Annual ACM Symposium on Parallelism in Algorithms and Architectures, San Diego, California, USA, June 911, 2007; 01/2007

Algorithms in Bioinformatics, 6th International Workshop, WABI 2006, Zurich, Switzerland, September 1113, 2006, Proceedings; 01/2006

Source Available from: Deshi Ye
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ABSTRACT: We study the online frequency allocation problem for wire less linear (highway) cellular networks, where the geographical coverage area is divided into cells aligned in a line. Calls arrive over time and are served by assigning frequencies to them, and no two calls emanating from the same cell or neighboring cells are assigned the same frequency. The objective is to minimize the span of frequencies used. In this paper we consider the problem with or without the assumption that calls have inflnite duration. If there is the assumption, we propose an algorithm with absolute competitive ratio of 3=2 and asymptotic com petitive ratio of 1:382. The lower bounds are also given: the absolute one is 3/2 and the asymptotic one is 4/3. Thus, our algorithm with absolute ratio of 3/2 is best possible. We also prove that the Greedy algorithm is 3=2competitive in both the absolute and asymptotic cases. For the problem without the assumption, i.e. calls may terminate at arbitrary time, we give the lower bounds for the competitive ratios: the absolute one is 5=3 and the asymptotic one is 14=9. We propose an optimal online algorithm with both competitive ratio of 5=3, which is better than the Greedy algorithm, with both competitive ratios 2. Algorithms and Computation, 17th International Symposium, ISAAC 2006, Kolkata, India, December 1820, 2006, Proceedings; 01/2006

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ABSTRACT: A con∞ictfree coloring for a given set of disks is a coloring of the disks such that for any point p on the plane there is a disk among the disks covering p having a color difierent from that of the rest of the disks that covers p. In the dynamic o†ine setting, a sequence of disks is given, we have to color the disks onebyone according to the order of the sequence and maintain the con∞ictfree property at any time for the disks that are colored. This paper focuses on unit disks, i.e., disks with radius one. We give an algorithm that colors a sequence of n unit disks in the dynamic o†ine setting using O(logn) colors. The algorithm is asymptotically optimal because ›(logn) colors is necessary to color some set of n unit disks for any value of n (8).