scholarly journals Robustness Computation of Dynamic Controllability in Probabilistic Temporal Networks with Ordinary Distributions

2020 ◽  
Author(s):  
Michael Saint-Guillain ◽  
Tiago Stegun Vaquero ◽  
Jagriti Agrawal ◽  
Steve Chien
Keyword(s):  
Probability Distributions ◽  
Dynamic Control ◽  
Success Probability ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Temporal Networks ◽  
Fixed Parameter ◽  
Probability Of Success ◽  
Dynamic Policy ◽  
Simple Temporal Networks

Most existing works in Probabilistic Simple Temporal Networks (PSTNs) base their frameworks on well-defined probability distributions. This paper addresses on PSTN Dynamic Controllability (DC) robustness measure, i.e. the execution success probability of a network under dynamic control. We consider PSTNs where the probability distributions of the contingent edges are ordinary distributed (e.g. non-parametric, non-symmetric). We introduce the concepts of dispatching protocol (DP) as well as DP-robustness, the probability of success under a predefined dynamic policy. We propose a fixed-parameter pseudo-polynomial time algorithm to compute the exact DP-robustness of any PSTN under NextFirst protocol, and apply to various PSTN datasets, including the real case of planetary exploration in the context of the Mars 2020 rover, and propose an original structural analysis.

scholarly journals Probabilistic Temporal Networks with Ordinary Distributions: Theory, Robustness and Expected Utility

2021 ◽  
Vol 71 ◽  
pp. 1091-1136
Author(s):  
Michael Saint-Guillain ◽  
Tiago Vaquero ◽  
Steve Chien ◽  
Jagriti Agrawal ◽  
Jordan Abrahams
Keyword(s):  
Expected Utility ◽  
Probability Distributions ◽  
Dynamic Control ◽  
Success Probability ◽  
Computation Method ◽  
Temporal Networks ◽  
Fixed Parameter ◽  
Simple Temporal Networks ◽  
Strong Dynamic ◽  
Utility Measures

Most existing works in Probabilistic Simple Temporal Networks (PSTNs) base their frameworks on well-defined, parametric probability distributions. Under the operational contexts of both strong and dynamic control, this paper addresses robustness measure of PSTNs, i.e. the execution success probability, where the probability distributions of the contingent durations are ordinary, not necessarily parametric, nor symmetric (e.g. histograms, PERT), as long as these can be discretized. In practice, one would obtain ordinary distributions by considering empirical observations (compiled as histograms), or even hand-drawn by field experts. In this new realm of PSTNs, we study and formally define concepts such as degree of weak/strong/dynamic controllability, robustness under a predefined dispatching protocol, and introduce the concept of PSTN expected execution utility. We also discuss the limitation of existing controllability levels, and propose new levels within dynamic controllability, to better characterize dynamic controllable PSTNs based on based practical complexity considerations. We propose a novel fixed-parameter pseudo-polynomial time computation method to obtain both the success probability and expected utility measures. We apply our computation method to various PSTN datasets, including realistic planetary exploration scenarios in the context of the Mars 2020 rover. Moreover, we propose additional original applications of the method.

scholarly journals Dynamic Control of Probabilistic Simple Temporal Networks

2020 ◽  
Vol 34 (06) ◽  
pp. 9851-9858
Author(s):  
Michael Gao ◽  
Lindsay Popowski ◽  
Jim Boerkoel
Keyword(s):  
Dynamic Scheduling ◽  
Dynamic Control ◽  
Probability Density Functions ◽  
Directed Search ◽  
Temporal Constraints ◽  
Temporal Networks ◽  
Loss Of Control ◽  
Dc Algorithm ◽  
Simple Temporal Networks ◽  
Real World Problems

The controllability of a temporal network is defined as an agent's ability to navigate around the uncertainty in its schedule and is well-studied for certain networks of temporal constraints. However, many interesting real-world problems can be better represented as Probabilistic Simple Temporal Networks (PSTNs) in which the uncertain durations are represented using potentially-unbounded probability density functions. This can make it inherently impossible to control for all eventualities. In this paper, we propose two new dynamic controllability algorithms that attempt to maximize the likelihood of successfully executing a schedule within a PSTN. The first approach, which we call Min-Loss DC, finds a dynamic scheduling strategy that minimizes loss of control by using a conflict-directed search to decide where to sacrifice the control in a way that optimizes overall success. The second approach, which we call Max-Gain DC, works in the other direction: it finds a dynamically controllable schedule and then attempts to progressively strengthen it by capturing additional uncertainty. Our approaches are the first known that work by finding maximally dynamically controllable schedules. We empirically compare our approaches against two existing PSTN offline dispatch approaches and one online approach and show that our Min-Loss DC algorithm outperforms the others in terms of maximizing execution success while maintaining competitive runtimes.

scholarly journals Deciding unitary equivalence between matrix polynomials and sets of bipartite quantum states

2011 ◽  
Vol 11 (9&10) ◽  
pp. 813-819
Author(s):  
Eric Chitambar ◽  
Carl Miller ◽  
Yaoyun Shi
Keyword(s):  
Success Probability ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Quantum States ◽  
Unitary Equivalence ◽  
Matrix Polynomials ◽  
Unitary Transformations ◽  
The Matrix ◽  
Pure States ◽  
High Success Probability

In this brief report, we consider the equivalence between two sets of $m+1$ bipartite quantum states under local unitary transformations. For pure states, this problem corresponds to the matrix algebra question of whether two degree $m$ matrix polynomials are unitarily equivalent; i.e. $UA_iV^\dagger=B_i$ for $0\leq i\leq m$ where $U$ and $V$ are unitary and $(A_i, B_i)$ are arbitrary pairs of rectangular matrices. We present a randomized polynomial-time algorithm that solves this problem with an arbitrarily high success probability and outputs transforming matrices $U$ and $V$.

APPROXIMATE BLOCK SORTING

2006 ◽  
Vol 17 (02) ◽  
pp. 337-355 ◽  
Author(s):  
MEENA MAHAJAN ◽  
RAGHAVAN RAMA ◽  
VENKATESH RAMAN ◽  
S. VIJAYKUMAR
Keyword(s):  
Approximation Algorithm ◽  
Optimization Problem ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Fixed Parameter Tractable ◽  
Identity Permutation ◽  
Fixed Parameter ◽  
Minimum Number ◽  
Increasing Sequences ◽  
Better Than

We consider the problem BLOCK-SORTING: Given a permutation, sort it by using a minimum number of block moves, where a block is a maximal substring of the permutation which is also a substring of the identity permutation, and a block move repositions the chosen block so that it merges with another block. Although this problem has recently been shown to be NP-hard [3], nothing better than a trivial 3-approximation was known. We present here the first non-trivial approximation algorithm to this problem. For this purpose, we introduce the following optimization problem: Given a set of increasing sequences of distinct elements, merge them into one increasing sequence with a minimum number of block moves. We show that the merging problem has a polynomial time algorithm. Using this, we obtain an O(n3) time 2-approximation algorithm for BLOCK-SORTING. We also observe that BLOCK-SORTING, as well as sorting by transpositions, are fixed-parameter-tractable in the framework of [6].

scholarly journals Quantum Algorithm for Attacking RSA Based on Fourier Transform and Fixed-Point

2021 ◽  
Vol 26 (6) ◽  
pp. 489-494
Author(s):  
Yahui WANG ◽  
Huanguo ZHANG
Keyword(s):  
Fixed Point ◽  
Polynomial Time ◽  
Multiplicative Group ◽  
Success Probability ◽  
Quantum Algorithm ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Rsa Cryptosystem ◽  
Shor's Algorithm ◽  
Quantum Polynomial

Shor in 1994 proposed a quantum polynomial-time algorithm for finding the order r of an element a in the multiplicative group Zn*, which can be used to factor the integer n by computing [see formula in PDF]and hence break the famous RSA cryptosystem. However, the order r must be even. This restriction can be removed. So in this paper, we propose a quantum polynomial-time fixed-point attack for directly recovering the RSA plaintext M from the ciphertext C, without explicitly factoring the modulus n. Compared to Shor’s algorithm, the order r of the fixed-point C for RSA(e, n) satisfying [see formula in PDF] does not need to be even. Moreover, the success probability of the new algorithm is at least [see formula in PDF] and higher than that of Shor’s algorithm, though the time complexity for both algorithms is about the same.

scholarly journals On Verifying and Maintaining Connectivity of Interval Temporal Networks

2019 ◽  
Vol 29 (02) ◽  
pp. 1950009 ◽  
Author(s):  
Eleni C. Akrida ◽  
Paul G. Spirakis
Keyword(s):  
Polynomial Time ◽  
High Speed ◽  
Information Dissemination ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Time Interval ◽  
Temporal Network ◽  
Temporal Networks ◽  
Tree Graphs ◽  
Time Period

An interval temporal network is, informally speaking, a network whose links change with time. The term interval means that a link may exist for one or more time intervals, called availability intervals of the link, after which it does not exist (until, maybe, a further moment in time when it starts being available again). In this model, we consider continuous time and high-speed (instantaneous) information dissemination. An interval temporal network is connected during a period of time [Formula: see text], if it is connected for all time instances [Formula: see text] (instantaneous connectivity). In this work, we study instantaneous connectivity issues of interval temporal networks. We provide a polynomial-time algorithm that answers if a given interval temporal network is connected during a time period. If the network is not connected throughout the given time period, then we also give a polynomial-time algorithm that returns large components of the network that remain connected and remain large during [Formula: see text]; the algorithm also considers the components of the network that start as large at time [Formula: see text] but dis-connect into small components within the time interval [Formula: see text], and answers how long after time [Formula: see text] these components stay connected and large. Finally, we examine a case of interval temporal networks on tree graphs where the lifetimes of links and, thus, the failures in the connectivity of the network are not controlled by us; however, we can “feed” the network with extra edges that may re-connect it into a tree when a failure happens, so that its connectivity is maintained during a time period. We show that we can with high probability maintain the connectivity of the network for a long time period by making these extra edges available for re-connection using a randomized approach. Our approach also saves some cost in the design of availabilities of the edges; here, the cost is the sum, over all extra edges, of the length of their availability-to-reconnect interval.

Learning Importance of Preferences

10.29007/v68w ◽  
2018 ◽  
Author(s):  
Ying Zhu ◽  
Mirek Truszczynski
Keyword(s):  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Scoring Rules ◽  
Np Hard ◽  
Individual Preferences

We study the problem of learning the importance of preferences in preference profiles in two important cases: when individual preferences are aggregated by the ranked Pareto rule, and when they are aggregated by positional scoring rules. For the ranked Pareto rule, we provide a polynomial-time algorithm that finds a ranking of preferences such that the ranked profile correctly decides all the examples, whenever such a ranking exists. We also show that the problem to learn a ranking maximizing the number of correctly decided examples (also under the ranked Pareto rule) is NP-hard. We obtain similar results for the case of weighted profiles when positional scoring rules are used for aggregation.

scholarly journals Metric Dimension Parameterized By Treewidth

Algorithmica ◽  
2021 ◽  
Author(s):  
Édouard Bonnet ◽  
Nidhi Purohit
Keyword(s):  
Computable Function ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Minimum Size ◽  
Metric Dimension ◽  
Resolving Set ◽  
Input Graph ◽  
Outerplanar Graphs ◽  
Bounded Treewidth ◽  
Fpt Algorithm

AbstractA resolving set S of a graph G is a subset of its vertices such that no two vertices of G have the same distance vector to S. The Metric Dimension problem asks for a resolving set of minimum size, and in its decision form, a resolving set of size at most some specified integer. This problem is NP-complete, and remains so in very restricted classes of graphs. It is also W[2]-complete with respect to the size of the solution. Metric Dimension has proven elusive on graphs of bounded treewidth. On the algorithmic side, a polynomial time algorithm is known for trees, and even for outerplanar graphs, but the general case of treewidth at most two is open. On the complexity side, no parameterized hardness is known. This has led several papers on the topic to ask for the parameterized complexity of Metric Dimension with respect to treewidth. We provide a first answer to the question. We show that Metric Dimension parameterized by the treewidth of the input graph is W[1]-hard. More refinedly we prove that, unless the Exponential Time Hypothesis fails, there is no algorithm solving Metric Dimension in time $$f(\text {pw})n^{o(\text {pw})}$$ f ( pw ) n o ( pw ) on n-vertex graphs of constant degree, with $$\text {pw}$$ pw the pathwidth of the input graph, and f any computable function. This is in stark contrast with an FPT algorithm of Belmonte et al. (SIAM J Discrete Math 31(2):1217–1243, 2017) with respect to the combined parameter $$\text {tl}+\Delta$$ tl + Δ , where $$\text {tl}$$ tl is the tree-length and $$\Delta$$ Δ the maximum-degree of the input graph.

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