Showing papers on "Average-case complexity published in 2018"
TL;DR: This work proposes a candidate assisted (CAN-A) optimal VNE algorithm with lower computational complexity, which reduces the mapping execution time substantially without performance loss and outperforms the typical heuristic algorithms in terms of other performance indices.
Abstract: Network virtualization (NV) is widely accepted as one enabling technology for future network, which enables multiple virtual networks (VNs) with different paradigms and protocols to coexist on the shared substrate network (SN). One key challenge in NV is VN embedding (VNE), which maps a VN onto the shared SN. Since VNE is NP-hard, existing efforts mainly focus on proposing heuristic algorithms that try to achieve feasible VNE in reasonable time, consequently the resulted embedding is not optimal. To tackle this difficulty, we propose a candidate assisted (CAN-A) optimal VNE algorithm with lower computational complexity. The key idea of the CAN-A algorithm lies in constructing the candidate substrate node subset and the candidate substrate path subset before embedding. This reduces the mapping execution time substantially without performance loss. In the following embedding, four types of node and link constraints are considered in the CAN-A algorithm, making it more applicable to realistic networks. Simulation results show that the execution time of CAN-A is hugely cut down compared with pure VNE-MIP algorithm. CAN-A also outperforms the typical heuristic algorithms in terms of other performance indices, such as the average VN request acceptance ratio and the average virtual link propagation delay.
69 citations
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TL;DR: In this paper, the role of Lloyd's computational bound in holographic complexity was investigated and a distinction between orthogonalizing and simple gates was made for diagnosing the complexity of black holes.
Abstract: In this note we investigate the role of Lloyd’s computational bound in holographic complexity. Our goal is to translate the assumptions behind Lloyd’s proof into the bulk language. In particular, we discuss the distinction between orthogonalizing and ‘simple’ gates and argue that these notions are useful for diagnosing holographic complexity. We show that large black holes constructed from series circuits necessarily employ simple gates, and thus do not satisfy Lloyd’s assumptions. We also estimate the degree of parallel processing required in this case for elementary gates to orthogonalize. Finally, we show that for small black holes at fixed chemical potential, the orthogonalization condition is satisfied near the phase transition, supporting a possible argument for the Weak Gravity Conjecture first advocated in [1].
68 citations
TL;DR: This work examines the complexity of inference in Bayesian networks specified by logical languages, and considers representations that range from fragments of propositional logic to function-free first-order logic with equality; in doing so it covers a variety of plate models and of probabilistic relational models.
8 citations
TL;DR: This article uses list coloring to model coloring with a fractional number of colors between χ − 1 and χ and turns out that the complexity follows an alternating three-dimensional pattern; understanding this pattern is very important for benchmarking purposes.
Abstract: It is known that the problem of deciding k-colorability of a graph exhibits an easy-hard-easy pattern,—that is, the average-case complexity for backtrack-type algorithms, as a function of k, has a peak. This complexity peak is either at k = χ − 1 or k = χ, where χ is the chromatic number of the graph. However, the behavior around the complexity peak is poorly understood. In this article, we use list coloring to model coloring with a fractional number of colors between χ − 1 and χ. We present a comprehensive computational study on the complexity of backtrack-type graph coloring algorithms in this critical range. According to our findings, an easy-hard-easy pattern can be observed on a finer scale between χ − 1 and χ as well. The highest complexity found this way can be higher than for any integer value of k. It turns out that the complexity follows an alternating three-dimensional pattern; understanding this pattern is very important for benchmarking purposes. Our results also answer the previously open question whether coloring with χ − 1 or with χ colors is harder: this depends on the location of the maximal fractional complexity.
5 citations
TL;DR: This paper obtains a logic called Quantitative Second Order Logics (QSO), and shows how some of its fragments can be used to capture fundamental counting complexity classes such as FP, #P and FPSPACE, among others.
Abstract: Descriptive Complexity has been very successful in characterizing complexity classes of decision problems in terms of the properties definable in some logics. However, descriptive complexity for counting complexity classes, such as FP and #P, has not been systematically studied, and it is not as developed as its decision counterpart. In this paper, we propose a framework based on Weighted Logics to address this issue. Specifically, by focusing on the natural numbers we obtain a logic called Quantitative Second Order Logics (QSO), and show how some of its fragments can be used to capture fundamental counting complexity classes such as FP, #P and FPSPACE, among others. We also use QSO to define a hierarchy inside #P, identifying counting complexity classes with good closure and approximation properties, and which admit natural complete problems. Finally, we add recursion to QSO, and show how this extension naturally captures lower counting complexity classes such as #L.
2 citations
TL;DR: In this article, the average case complexity of the number of iterations of Shellsort has been shown to be upper bounded by the Jiang-Li-Vitanyi lower bound.
Abstract: We prove a lower bound expressed in the increment se-
quence on the average-case complexity of the number of
inversions of Shellsort. This lower bound is sharp in every
case where it could be checked. A special case of this lower
bound yields the general Jiang-Li-Vitanyi lower bound. We
obtain new results, for example, determining the average-
case complexity precisely in the Yao-Janson-Knuth 3-pass
case.
1 citations
01 Oct 2018
TL;DR: In this paper, a maximum induced matching algorithm for permutation graphs was proposed, which has better time complexity than the best known algorithm in both worst case and average case, where k(G) is the cardinality of the minimum clique cover set.
Abstract: Let $G = (V,~E)$ be an undirected graph, where V is the vertex set and E is the edge set. A subset M of E is an induced matching of G if M is a matching of G and no two edges in M are joined by an edge. Finding a maximum induced matching is a $\mathbb {N}\mathbb {P}$-Hard problem on general graphs, even on bipartite graphs. However, this problem can be solved in polynomial time in some special graph classes such as weakly chordal, chordal, interval and circular-arc graphs. In this paper, we introduce a maximum induced matching algorithm in permutation graphs with $O(|V|k(G)\log \log (|V|))$ time in worst case complexity and $O(|V|\sqrt {|V|}\log \log (|V|))$ time in average case complexity, where $k(G)$ is the cardinality of the minimum clique cover set. The approach is to reduce the size of vertex set of $L(G)^{2}$ without changing the cardinality of its maximum independent set. Our algorithm has better time complexity than the best known algorithm in both worst case and average case.
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TL;DR: This work generalizes the original Leapfrogging Samplesort to a sorted sample of size $s$ and an unsorted part of size $(2^k-1)(s+1)$, and shows that the worst-case complexity is $O(n \log^2 n)$ and the average- case complexity is O(n)\log n).
Abstract: The original Leapfrogging Samplesort operates on a sorted sample of size $s$ and an unsorted part of size $s+1$. We generalize this to a sorted sample of size $s$ and an unsorted part of size $(2^k-1)(s+1)$, where $k = O(1)$. We present a practical implementation of this class of algorithms and we show that the worst-case complexity is $O(n \log^2 n)$ and the average-case complexity is $O(n \log n)$.
Keywords: Samplesort, Quicksort, Leapfrogging Samplesort, sorting, analysis of algorithms.
TL;DR: Correct order estimates of the average-case complexity of functions with maximum average- case complexity among all underdetermined functions are derived depending on the degree of their determinacy, thesize of their domain, and the size of their support.
Abstract: Abstract The average-case complexity of computation of underdetermined functions by straight-line programs with conditional stop over the basis of all at most two-place Boolean functions is considered. Correct order estimates of the average-case complexity of functions with maximum average-case complexity among all underdetermined functions are derived depending on the degree of their determinacy, the size of their domain, and the size of their support.
31 Jan 2018
TL;DR: In this paper, Chakraborty et al. investigated the parameterized complexity of three sorting algorithms, namely, Quick sort, Heap sort and K-sort, with the same average case complexity O(Nlog2N) for the quasi binomial input parameters.
Abstract: Parameterized complexity is one of the important concepts that has emerged in the recent past in the field of computer science. It has been observed that for certain algorithms such as sorting, the parameters of the input distribution characterizing the sorting elements are very crucial in explaining the complexity of an algorithm (see Anchala, Chakraborty (2007,2008), Chakraborty&Sourabh,(2007)).The present paper investigates the parameterized complexity of three sorting algorithms namely, Quick sort, Heap sort and K-sort ( with the same average case complexity O(Nlog2N)), for the quasi binomial input parameters and compares the results with those for binomial input parameters.