Graph partitioning is a key fundamental problem in the area of big graph computation. Previous works do not consider the practical requirements when optimizing the big data analysis in real applications. In this paper...
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PCA WITH OUTLIERS is the fundamental problem of identifying an underlying low-dimensional subspace in a data set corrupted with outliers. A large body of work is devoted to the information-theoretic aspects of this pr...
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ISBN:
(纸本)9781713845065
PCA WITH OUTLIERS is the fundamental problem of identifying an underlying low-dimensional subspace in a data set corrupted with outliers. A large body of work is devoted to the information-theoretic aspects of this problem. However, from the computational perspective, its complexity is still not well-understood. We study this problem from the perspective of parameterized complexity by investigating how parameters like the dimension of the data, the subspace dimension, the number of outliers and their structure, and approximation error, influence the computational complexity of the problem. Our algorithmic methods are based on techniques of randomized linear algebra and algebraic geometry.
Understanding how different two organisms are is one question addressed by the comparative genomics field. A well-accepted way to estimate the evolutionary distance between genomes of two organisms is finding the rear...
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Understanding how different two organisms are is one question addressed by the comparative genomics field. A well-accepted way to estimate the evolutionary distance between genomes of two organisms is finding the rearrangement distance, which is the smallest number of rearrangements needed to transform one genome into another. By representing genomes as permutations, one of them can be represented as the identity permutation, and, so, we reduce the problem of transforming one permutation into another to the problem of sorting a permutation using the minimum number of rearrangements. This work investigates the problems of sorting permutations using reversals and/or transpositions, with some additional restrictions of biological relevance. Given a value lambda, the problem now is how to sort a lambda-permutation, which is a permutation whose elements are less than lambda positions away from their correct places (regarding the identity), by applying the minimum number of rearrangements. Each lambda-rearrangement must have size, at most, lambda, and, when applied to a lambda-permutation, the result should also be a lambda-permutation. We present algorithms with approximation factors of O(lambda(2)), O(lambda), and O(1) for the problems of Sorting lambda-Permutations by lambda-Reversals, by lambda-Transpositions, and by both operations.
Given an undirected graph, G, and vertices, s and t in G, the tracking paths problem is that of finding the smallest subset of vertices in G whose intersection with any s-t path results in a unique sequence. This prob...
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ISBN:
(纸本)9783030835088;9783030835071
Given an undirected graph, G, and vertices, s and t in G, the tracking paths problem is that of finding the smallest subset of vertices in G whose intersection with any s-t path results in a unique sequence. This problem is known to be NP-complete and has applications to animal migration tracking and detecting marathon course-cutting, but its approximability is largely unknown. In this paper, we address this latter issue, giving novel algorithms having approximation ratios of (1+epsilon), O(lg OPT) and O(lg n), for H-minor-free, general, and weighted graphs, respectively. We also give a linear kernel for H-minor-free graphs.
In the problem of active sequential hypothesis testing (ASHT), a learner seeks to identify the true hypothesis from among a known set of hypotheses. The learner is given a set of actions and knows the random distribut...
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ISBN:
(纸本)9781713845393
In the problem of active sequential hypothesis testing (ASHT), a learner seeks to identify the true hypothesis from among a known set of hypotheses. The learner is given a set of actions and knows the random distribution of the outcome of any action under any true hypothesis. Given a target error delta > 0, the goal is to sequentially select the fewest number of actions so as to identify the true hypothesis with probability at least 1 - delta. Motivated by applications in which the number of hypotheses or actions is massive (e.g., genomics-based cancer detection), we propose efficient (greedy, in fact) algorithms and provide the first approximation guarantees for ASHT, under two types of adaptivity. Both of our guarantees are independent of the number of actions and logarithmic in the number of hypotheses. We numerically evaluate the performance of our algorithms using both synthetic and real-world DNA mutation data, demonstrating that our algorithms outperform previously proposed heuristic policies by large margins.
We study the heterogeneous weighted delivery (HWD) problem introduced in [Bartschi et al., STACS'17] where k heterogeneous mobile agents (e.g., robots, vehicles, etc.), initially positioned on vertices of an n-ver...
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ISBN:
(纸本)9783030795269;9783030795276
We study the heterogeneous weighted delivery (HWD) problem introduced in [Bartschi et al., STACS'17] where k heterogeneous mobile agents (e.g., robots, vehicles, etc.), initially positioned on vertices of an n-vertex edge-weighted graph G, have to deliver m messages. Each message is initially placed on a source vertex of G and needs to be delivered to a target vertex of G. Each agent can move along the edges of G and carry at most one message at any time. Each agent has a rate of energy consumption per unit of traveled distance and the goal is that of delivering all messages using the minimum overall amount of energy. This problem has been shown to be NP-hard even when k = 1, and is 4 rho-approximable where rho is the ratio between the maximum and minimum energy consumption of the agents. In this paper, we provide approximation algorithms with approximation ratios independent of the energy consumption rates. First, we design a polynomial-time 8approximation algorithm for k = O(root log n), closing a problem left open in [Bartschi et al., ATMOS'17]. This algorithm can be turned into a O(k)-approximation algorithm that always runs in polynomial-time, regardless of the values of k. Then, we show that HWD problem is 36-approximable in polynomial-time when each agent has one of two possible consumption rates. Finally, we design a polynomial-time (O) over tilde (log(3) n)-approximation algorithm for the general case.
Structural balance theory is an important theory in signed graphs. We consider the optimization problems: given a signed graph, the maximum number of edges that needed to be kept to make it balanced is called K(G). We...
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In this paper, we introduce the lower-bounded knapsack median problem (LB knapsack median). In this problem, we are given a set of facilities, a set of clients, a budget B and a lower bound L. Every facility is associ...
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Let G = (V, E) be a graph. Then the achromatic number for the graph is the largest integer m in such a way that there is a partition of V into disjoint independent sets (V1, V2 …, Vm) satisfying the condition that fo...
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Biological computation is the field that studies the computations performed by the biological systems and includes the development of algorithms or other computational techniques inspired by nature. The genome rearran...
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