It is incumbent on power system managers, designers, planners and operators to ensure that customers receive adequate and secure supplies within reasonable economic constraints. Historically, this has been assessed us...
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It is incumbent on power system managers, designers, planners and operators to ensure that customers receive adequate and secure supplies within reasonable economic constraints. Historically, this has been assessed using deterministic criteria, techniques and indices. Although the application of probability theory has been continuously developed since the 1930s, it is only relatively recently that the techniques, data and computational resources have reached the stage where they are directly applicable to practical planning and operational decision making. This paper discusses reliability assessment and related issues for power system hierarchical level III, the power distribution system.
Discovering patterns in biological sequences is very important to extract useful information from them. Motifs are crucial patterns that have numerous applications including the identification of transcription factors...
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ISBN:
(纸本)9781509016129
Discovering patterns in biological sequences is very important to extract useful information from them. Motifs are crucial patterns that have numerous applications including the identification of transcription factors and their binding sites, composite regulatory patterns, similiarity between families of proteins, etc. Several models of motifs have been proposed in the literature. The (l,d)-motif model is one of these that has been studied widely. The (l,d)-motif search problem is also known as Planted Motif Search (PMS). The general problem of PMS has been proven to be NP-hard. In this paper, we present an elegant as well as efficient randomized algorithm, named qPMS10, to solve PMS. Currently, the best known algorithm for solving PMS is qPMS9 and it can solve challenging (l, d)-motif instances up to (28,12) and (30,13). qPMS9 is a deterministic algorithm. We provide a performance comparison of qPMS10 with qPMS9 on standard benchmark datasets. Both theoretical and empirical analysis demonstrate that our randomized algorithm outperforms the exsiting algorithms for solving PMS. Besides, the random sampling techniques we employ in our algorithm can also be extended to solve other motif search problems including Simple Motif Search (SMS) and Edit-distance based Motif Search (EMS). Furthermore, our algorithm can be parallelized efficiently and has the potential of yielding great speedups on multi-core machines.
Starting with with work of Michail et al., the problem of Counting the number of nodes in Anonymous Dynamic Networks has attracted a lot of attention. The problem is challenging because nodes are indistinguishable (th...
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Starting with with work of Michail et al., the problem of Counting the number of nodes in Anonymous Dynamic Networks has attracted a lot of attention. The problem is challenging because nodes are indistinguishable (they lack identifiers and execute the same program), and the topology may change arbitrarily from round to round of communication, as long as the network is connected in each round. The problem is central in distributed computing, as the number of participants is frequently needed to make important decisions, including termination, agreement, synchronization, among others. A variety of distributed algorithms built on top of mass-distribution techniques have been presented, analyzed, and experimentally evaluated;some of them assumed additional knowledge of network characteristics, such as bounded degree or given upper bound on the network size. However, the question of whether Counting can be solved deterministically in sub-exponential time remained open. In this work, we answer this question positively by presenting Methodical Counting, which runs in polynomial time and requires no knowledge of network characteristics. Moreover, we also show how to extend Methodical Counting to compute the sum of input values and more complex functions without extra cost. Our analysis leverages previous work on random walks in evolving graphs, combined with carefully chosen alarms in the algorithm that control the process and its parameters. To the best of our knowledge, our Counting algorithm and its extensions to other algebraic and Boolean functions are the first that can be implemented in practice with worst-case guarantees.
This paper presents new results in external memory for finding the skyline (a.k.a. maxima) of N points in d-dimensional space. The state of the art uses O((N/B)log_(M/B)~(d-2)(N/B)) I/Os for fixed d ≥ 3, and O((N/B)l...
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ISBN:
(纸本)9781627484855
This paper presents new results in external memory for finding the skyline (a.k.a. maxima) of N points in d-dimensional space. The state of the art uses O((N/B)log_(M/B)~(d-2)(N/B)) I/Os for fixed d ≥ 3, and O((N/B)log_(M/B)(N/B)) I/Os for d = 2, where M and B are the sizes (in words) of memory and a disk block, respectively. We give algorithms whose running time depends on the number K of points in the skyline. Specifically, we achieve O((N/B) log_(M/B)~(d-2)(K/B)) expected cost for fixed d ≥ 3, and O((N/B) log_(M/B) (K/B)) worst-case cost for d = 2. As a side product, we solve two problems both of independent interest. The first one, the M-skyline problem, aims at reporting M arbitrary skyline points, or the entire skyline if its size is at most M. We settle this problem in O(N/B) expected time in any fixed dimensionality d. The second one, the M -pivot problem, is more fundamental: given a set S of N elements drawn from an ordered domain, it outputs M evenly scattered elements (called pivots) from S, namely, S has asymptotically the same number of elements between each pair of consecutive pivots. We give a deterministic algorithm for solving the problem in O(N/B) I/Os.
We give a deterministic algorithm to find the minimum cut in a surface-embedded graph in near-linear time. Given an undirected graph embedded on an orientable surface of genus g, our algorithm computes the minimum cut...
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ISBN:
(纸本)9781611972108
We give a deterministic algorithm to find the minimum cut in a surface-embedded graph in near-linear time. Given an undirected graph embedded on an orientable surface of genus g, our algorithm computes the minimum cut in g~(O(g))n log log n time, matching the running time of the fastest algorithm known for planar graphs, due to Lacki and Sankowski, for any constant g. Indeed, our algorithm calls Lacki and Sankowski's recent O(n log log n) time planar algorithm as a subroutine. Previously, the best time bounds known for this problem followed from two algorithms for general sparse graphs: a randomized algorithm of Karger that runs in O(n log~3 n) time and succeeds with high probability, and a deterministic algorithm of Nagamochi and Ibaraki that runs in O(n~2 log n) time. We can also achieve a deterministic g~(O(g))n~2 log log n time bound by repeatedly applying the best known algorithm for minimum (s, t)-cuts in surface graphs. The bulk of our work focuses on the case where the dual of the minimum cut splits the underlying surface into multiple components with positive genus.
In this paper we propose a deterministic algorithm to produce a set of diverse paths between a given start and goal configuration in 3D environments. These diverse paths have the following properties: 1) They are boun...
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ISBN:
(纸本)9781467363563
In this paper we propose a deterministic algorithm to produce a set of diverse paths between a given start and goal configuration in 3D environments. These diverse paths have the following properties: 1) They are bounded in length and 2) They are non-visibility-deformable into one another. Maintaining multiple path alternatives is important in practical applications such as planning in dynamic environments, in which a path may unexpectedly become infeasible due to unforeseen environmental changes. We present our approach, the distance cost considered (based on the path deformability concept previously introduced in [11]) and finally show results of simulated experiments that exemplify the effectiveness of our algorithm.
The online (uniform) buy-at-bulk network design problem asks us to design a network, where the edge-costs exhibit economy-of-scale. Previous approaches to this problem used tree-embeddings, giving us randomized algori...
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ISBN:
(纸本)9781510836358
The online (uniform) buy-at-bulk network design problem asks us to design a network, where the edge-costs exhibit economy-of-scale. Previous approaches to this problem used tree-embeddings, giving us randomized algorithms. Moreover, the optimal results with a logarithmic competitive ratio requires the metric on which the network is being built to be known up-front; the competitive ratios then depend on the size of this metric (which could be much larger than the number of terminals that arrive). We consider the buy-at-bulk problem in the least restrictive model where the metric is not known in advance, but revealed in parts along with the demand points seeking connectivity arriving online. For the single sink buy-at-bulk problem, we give a deterministic online algorithm with competitive ratio that is logarithmic in k, the number of terminals that have arrived, matching the lower bound known even for the online Steiner tree problem. In the oblivious case when the buy-at-bulk function used to compute the edge-costs of the network is not known in advance (but is the same across all edges), we give a deterministic algorithm with competitive ratio polylogarithmic in k, the number of terminals. At the heart of our algorithms are optimal constructions for online Light Approximate Shortest-path Trees (LASTs) and spanners, and their variants. We give constructions that have optimal trade-offs in terms of cost and stretch. We also define and give constructions for a new notion of LASTs where the set of roots (in addition to the points) expands over time. We expect these techniques will find applications in other online network-design problems.
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