The board game Fragmind(TM) poses the following problem: The player has to reconstruct an (unknown) string s over the alphabet Sigma. To this end, the game reports the following information to the player, for every ch...
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The board game Fragmind(TM) poses the following problem: The player has to reconstruct an (unknown) string s over the alphabet Sigma. To this end, the game reports the following information to the player, for every character x is an element of Sigma: First, the string s is cleaved wherever the character x is found in s. Second, every resulting fragment y is scrambled by a random permutation so that the only information left is how many times y contains each character sigma is an element of Sigma. These scrambled fragments are then reported to the player. Clearly, distinct strings can show identical cleavage patterns for all cleavage characters. In fact, even short strings of length 30+ usually have non-unique cleavage patterns. To this end, we introduce a generalization of the game setup called Sequencing from Compomers. We also generate those fragments of s that contain up to k uncleaved characters x, for some small and fixed threshold k. This modification dramatically increases the length of strings that can be uniquely reconstructed. We show that it is NP-hard to decide whether there exists some string compatible with the input data, but we also present a branch-and-bound runtime heuristic to find all such strings: The input data are transformed into subgraphs of the de Bruijn graph, and we search for walks in these subgraphs simultaneously. The above problem stems from the analysis of mass spectrometry data from base-specific cleavage of DNA sequences, and gives rise to a completely new approach to DNA de-novo sequencing.
We consider two multicriteria versions of the global minimum cut problem in undirected graphs. In the k-criteria setting, each edge of the input graph has k non-negative costs associated with it. These costs are measu...
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ISBN:
(纸本)9783540241317
We consider two multicriteria versions of the global minimum cut problem in undirected graphs. In the k-criteria setting, each edge of the input graph has k non-negative costs associated with it. These costs are measured in separate, non-interchangeable, units. In the AND-version of the problem, purchasing an edge requires the payment of all the k costs associated with it. In the OR-version, an edge can be purchased by paying any one of the k costs associated with it. Given k bounds b(1),b(2),. . . ,b(k), the basic multicriteria decision problem is whether there exists a cut C of the graph that can be purchased using a budget of b(i) units of the ith criterion, for 1 <= i <= k. We show that the AND-version of the multicriteria global minimum cut problem is polynomial for any fixed number k of criteria. The OR-version of the problem, on the other hand, is NP-hard even for k = 2, but can be solved in pseudo-polynomial time for any fixed number k of criteria. It also admits an FPTAS. Further extensions, some applications, and multicriteria versions of two other optimization problems are also discussed.
The classic view of metabolism as a collection of metabolic pathways is being questioned with the currently available possibility of studying whole networks. Novel ways of decomposing the network into modules and moti...
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The classic view of metabolism as a collection of metabolic pathways is being questioned with the currently available possibility of studying whole networks. Novel ways of decomposing the network into modules and motifs that could be considered as the building blocks of a network are being suggested. In this work, we introduce a new definition of motif in the context of metabolic networks. Unlike in previous works on (other) biochemical networks, this definition is not based only on topological features. We propose instead to use an alternative definition based on the functional nature of the components that form the motif, which we call a reaction motif. After introducing a formal framework motivated by biological considerations, we present complexity results on the problem of searching for all occurrences of a reaction motif in a network and introduce an algorithm that is fast in practice in most situations. We then show an initial application to the study of pathway evolution. Finally, we give some general features of the observed number of occurrences in order to highlight some structural features of metabolic networks.
In this paper the modification of classic algorithm finding the optimum way of passing connection in a network with the fuzzy set theory is presented. The resulted modification allows to optimize time of establishment...
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ISBN:
(纸本)9781424413218
In this paper the modification of classic algorithm finding the optimum way of passing connection in a network with the fuzzy set theory is presented. The resulted modification allows to optimize time of establishment of connection in a network taking into account unclear of data about the delay of signal in nodes.
We present a simple algorithm which maintains the topological order of a directed acyclic graph with n nodes under an online edge insertion sequence in O (n2.75) time, independent of the number of edges m inserted. Fo...
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The high number of false positive alarms that are generated in large intrusion detection infrastructures makes it difficult for operations staff to separate false alerts from real attacks. One means of reducing this p...
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ISBN:
(纸本)354039723X
The high number of false positive alarms that are generated in large intrusion detection infrastructures makes it difficult for operations staff to separate false alerts from real attacks. One means of reducing this problem is the use of meta alarms, or rules, which identify known attack patterns in alarm streams. The obvious risk with this approach is that the rule base may not be complete with respect to every true attack profile, especially those which are new. Currently, new rules are discovered manually, a process which is both costly and error prone. We present a novel approach using association rule mining to shorten the time that elapses from the appearance of a new attack profile in the data to its definition as a rule in the production monitoring infrastructure.
graph algorithms axe widely used in VLSI CAD. Traditional graph algorithms can handle graphs with deterministic edge weights. As VLSI technology continues to scale into nanometer designs, we need to use probability di...
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ISBN:
(纸本)0780394518
graph algorithms axe widely used in VLSI CAD. Traditional graph algorithms can handle graphs with deterministic edge weights. As VLSI technology continues to scale into nanometer designs, we need to use probability distributions for edge weights in order to model uncertainty due to parameter variations. In this paper, we consider the statistical shortest path (SSP) problem. Given a graph G, the edge weights of G axe random variables. For each path P in G, let L-P be its length, which is the sum of all edge weights on P. Clearly L-P is a random variable and we let mu(p) and sigma(2)(p) be its mean and variance, respectively. In the SSP problem, our goal is to find a path P connecting two given vertices to minimize the cost function mu(p) + Phi(sigma(2)(p)) where Phi is an arbitrary function. (For example, if Phi(x) = 3 root x, the cost function is mu(p) + 3 sigma(p).) To minimize uncertainty in the final result, it is meaningful to look for paths with bounded variance, i.e., sigma(2)(p) <= B for a given fixed bound B. In this paper, we present an exact algorithm to solve the SSP problem in O(B(V + E)) time where V and E axe the numbers of vertices and edges, respectively, in G. Our algorithm is superior to previous algorithms for SSP problem because we can handle: 1) general graphs (unlike previous works applicable only to directed acyclic graphs), 2) arbitrary edge-weight distributions (unlike previous algorithms designed only for specific distributions such as Gaussian), and 3) general cost function (none of the previous algorithms can even handle the cost function mu(p) + 3 sigma(p). Finally, we discuss applications of the SSP problem to maze routing, buffer insertions, and timing analysis under parameter variations.
There are three fundamental online problems in robotics: navigation/search, localization, and exploration. Constructing a complete map of an unknown environment while using a short path is the task of autonomous robot...
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There are three fundamental online problems in robotics: navigation/search, localization, and exploration. Constructing a complete map of an unknown environment while using a short path is the task of autonomous robots when they have to explore a whole environment. Besides the practical problems that arise when an autonomous robot needs to travel through real terrain there is the question of how well the robot will perform compared to an optimal strategy that has complete knowledge of the environment and can plan an exploration path in advance. The robot must always decide its further movements online and with only partial knowledge of the already explored environment. Different models of the environment lead to different algorithms that try to cope with the difficulties given by a particular modeling. The advantage of modeling environments as graphs lies in the fact that the geometric features are neglected and one can concentrate on the combinatorial aspects of the exploration problem. While we are focusing on directed graphs in the case of exploration we consider both directed and undirected graphs for the search problem, in which the robot needs to find a specific goal. The thesis begins with a short explanation of the motivation behind online search and exploration. We survey existing algorithms, involving a detailed discussion of some of those algorithms, which---or parts of which---are reused in some of our algorithms. The thesis continues with the study of the problem of exploring an unknown, strongly connected directed graph G. Starting at some vertex of the graph, we must visit every edge and every vertex at least once. The goal is to minimize the number of edge traversals. It is known that the competitive ratio of online algorithms for this problem depends on the deficiency d of the graph, which is the minimum number of edges that must be added to make the graph Eulerian. We present the first deterministic online exploration algorithm whose competitive ra
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