scholarly journals Probabilistic Deduction with Conditional Constraints over Basic Events

1999 ◽  
Vol 10 ◽  
pp. 199-241 ◽  
Author(s):  
T. Lukasiewicz
Keyword(s):  
Polynomial Time ◽  
Linear Time ◽  
Linear Programs ◽  
Np Hard ◽  
Global Approach ◽  
Local Approach ◽  
Nonlinear Programs ◽  
Equivalent Linear ◽  
Special Case

We study the problem of probabilistic deduction with conditional constraints over basic events. We show that globally complete probabilistic deduction with conditional constraints over basic events is NP-hard. We then concentrate on the special case of probabilistic deduction in conditional constraint trees. We elaborate very efficient techniques for globally complete probabilistic deduction. In detail, for conditional constraint trees with point probabilities, we present a local approach to globally complete probabilistic deduction, which runs in linear time in the size of the conditional constraint trees. For conditional constraint trees with interval probabilities, we show that globally complete probabilistic deduction can be done in a global approach by solving nonlinear programs. We show how these nonlinear programs can be transformed into equivalent linear programs, which are solvable in polynomial time in the size of the conditional constraint trees.

scholarly journals Deception through Half-Truths

2020 ◽  
Vol 34 (06) ◽  
pp. 10110-10117
Author(s):  
Andrew Estornell ◽  
Sanmay Das ◽  
Yevgeniy Vorobeychik
Keyword(s):  
Polynomial Time ◽  
Transition Function ◽  
Np Hard ◽  
Fundamental Issue ◽  
Fake News ◽  
False Information ◽  
Important Special Case ◽  
Bayes Network ◽  
Special Case

Deception is a fundamental issue across a diverse array of settings, from cybersecurity, where decoys (e.g., honeypots) are an important tool, to politics that can feature politically motivated “leaks” and fake news about candidates. Typical considerations of deception view it as providing false information. However, just as important but less frequently studied is a more tacit form where information is strategically hidden or leaked. We consider the problem of how much an adversary can affect a principal's decision by “half-truths”, that is, by masking or hiding bits of information, when the principal is oblivious to the presence of the adversary. The principal's problem can be modeled as one of predicting future states of variables in a dynamic Bayes network, and we show that, while theoretically the principal's decisions can be made arbitrarily bad, the optimal attack is NP-hard to approximate, even under strong assumptions favoring the attacker. However, we also describe an important special case where the dependency of future states on past states is additive, in which we can efficiently compute an approximately optimal attack. Moreover, in networks with a linear transition function we can solve the problem optimally in polynomial time.

scholarly journals Converging from branching to linear metrics on Markov chains

2017 ◽  
Vol 29 (1) ◽  
pp. 3-37 ◽  
Author(s):  
GIORGIO BACCI ◽  
GIOVANNI BACCI ◽  
KIM G. LARSEN ◽  
RADU MARDARE
Keyword(s):  
Model Checking ◽  
Markov Chains ◽  
Temporal Logic ◽  
Polynomial Time ◽  
Linear Time ◽  
Linear Temporal Logic ◽  
Np Hard ◽  
Branching Time ◽  
Threshold Problem ◽  
Ltl Model Checking

We study two well-known linear-time metrics on Markov chains (MCs), namely, the strong and strutter trace distances. Our interest in these metrics is motivated by their relation to the probabilistic linear temporal logic (LTL)-model checking problem: we prove that they correspond to the maximal differences in the probability of satisfying the same LTL and LTL−X(LTL without next operator) formulas, respectively.The threshold problem for these distances (whether their value exceeds a given threshold) is NP-hard and not known to be decidable. Nevertheless, we provide an approximation schema where each lower and upper approximant is computable in polynomial time in the size of the MC.The upper approximants are bisimilarity-like pseudometrics (hence, branching-time distances) that converge point-wise to the linear-time metrics. This convergence is interesting in itself, because it reveals a non-trivial relation between branching and linear-time metric-based semantics that does not hold in equivalence-based semantics.

A POLYNOMIAL-TIME ALGORITHM FOR COMPUTING THE RESILIENCE OF ARRANGEMENTS OF RAY SENSORS

2014 ◽  
Vol 24 (03) ◽  
pp. 225-236 ◽  
Author(s):  
DAVID KIRKPATRICK ◽  
BOTING YANG ◽  
SANDRA ZILLES
Keyword(s):  
Polynomial Time ◽  
Linear Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
The Other ◽  
Np Hard ◽  
Sensor Coverage ◽  
Entire Plane ◽  
Line Segments ◽  
Minimum Number

Given an arrangement A of n sensors and two points s and t in the plane, the barrier resilience of A with respect to s and t is the minimum number of sensors whose removal permits a path from s to t such that the path does not intersect the coverage region of any sensor in A. When the surveillance domain is the entire plane and sensor coverage regions are unit line segments, even with restricted orientations, the problem of determining the barrier resilience is known to be NP-hard. On the other hand, if sensor coverage regions are arbitrary lines, the problem has a trivial linear time solution. In this paper, we study the case where each sensor coverage region is an arbitrary ray, and give an O(n2m) time algorithm for computing the barrier resilience when there are m ⩾ 1 sensor intersections.

scholarly journals Polynomial time recognition of vertices contained in all (or no) maximum dissociation sets of a tree

2021 ◽  
Vol 7 (1) ◽  
pp. 569-578
Author(s):  
Jianhua Tu ◽  
◽  
Lei Zhang ◽  
Junfeng Du ◽  
Rongling Lang ◽  
...  
Keyword(s):  
Polynomial Time ◽  
Linear Time ◽  
Bipartite Graphs ◽  
Recognition Algorithm ◽  
Vertex Degree ◽  
Np Hard ◽  
Maximum Cardinality

<abstract><p>In a graph $ G $, a dissociation set is a subset of vertices which induces a subgraph with vertex degree at most 1. Finding a dissociation set of maximum cardinality in a graph is NP-hard even for bipartite graphs and is called the maximum dissociation set problem. The complexity of the maximum dissociation set problem in various sub-classes of graphs has been extensively studied in the literature. In this paper, we study the maximum dissociation problem from different perspectives and characterize the vertices belonging to all maximum dissociation sets, and no maximum dissociation set of a tree. We present a linear time recognition algorithm which can determine whether a given vertex in a tree is contained in all (or no) maximum dissociation sets of the tree. Thus for a tree with $ n $ vertices, we can find all vertices belonging to all (or no) maximum dissociation sets of the tree in $ O(n^2) $ time.</p></abstract>

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.

On the Complexity of Deadlock Recovery

1986 ◽  
Vol 9 (3) ◽  
pp. 323-342
Author(s):  
Joseph Y.-T. Leung ◽  
Burkhard Monien
Keyword(s):  
Computational Complexity ◽  
Polynomial Time ◽  
Arbitrary Number ◽  
The Other ◽  
Np Hard ◽  
Total Cost ◽  
Other Hand ◽  
Input Parameters ◽  
Resource Type

We consider the computational complexity of finding an optimal deadlock recovery. It is known that for an arbitrary number of resource types the problem is NP-hard even when the total cost of deadlocked jobs and the total number of resource units are “small” relative to the number of deadlocked jobs. It is also known that for one resource type the problem is NP-hard when the total cost of deadlocked jobs and the total number of resource units are “large” relative to the number of deadlocked jobs. In this paper we show that for one resource type the problem is solvable in polynomial time when the total cost of deadlocked jobs or the total number of resource units is “small” relative to the number of deadlocked jobs. For fixed m ⩾ 2 resource types, we show that the problem is solvable in polynomial time when the total number of resource units is “small” relative to the number of deadlocked jobs. On the other hand, when the total number of resource units is “large”, the problem becomes NP-hard even when the total cost of deadlocked jobs is “small” relative to the number of deadlocked jobs. The results in the paper, together with previous known ones, give a complete delineation of the complexity of this problem under various assumptions of the input parameters.

Optimal Order Picking in Carousels Storage System

2012 ◽  
Vol 601 ◽  
pp. 347-353
Author(s):  
Xiong Zhi Wang ◽  
Guo Qing Wang
Keyword(s):  
Approximation Algorithm ◽  
General Problem ◽  
Storage System ◽  
Order Picking ◽  
Total Order ◽  
Experimental Results ◽  
Optimal Order ◽  
Np Hard ◽  
Special Case

We study the order picking problem in carousels system with a single picker. The objective is to find a picking scheduling to minimizing the total order picking time. After showing the problem being strongly in NP-Hard and finding two characteristics, we construct an approximation algorithm for a special case (two carousels) and a heuristics for the general problem. Experimental results verify that the solutions are quickly and steadily achieved and show its better performance.

scholarly journals In some curved spaces, one can solve NP-hard problems in polynomial time

2009 ◽  
Vol 158 (5) ◽  
pp. 727-740 ◽  
Author(s):  
V. Kreinovich ◽  
M. Margenstern
Keyword(s):  
Polynomial Time ◽  
Np Hard ◽  
Curved Spaces ◽  
Hard Problems ◽  
Np Hard Problems

Iterated Local Search and Other Algorithms for Buffered Two-Machine Permutation Flow Shops with Constant Processing Times on One Machine

2020 ◽  
pp. 1-25
Author(s):  
Hoang Thanh Le ◽  
Philine Geser ◽  
Martin Middendorf
Keyword(s):  
Local Search ◽  
Flow Shop ◽  
Iterated Local Search ◽  
Flow Shop Scheduling ◽  
Np Hard ◽  
Ant Colony Optimization Algorithm ◽  
Solution Quality ◽  
Processing Times ◽  
One Machine ◽  
Special Case

The two-machine permutation flow shop scheduling problem with buffer is studied for the special case that all processing times on one of the two machines are equal to a constant c. This case is interesting because it occurs in various applications, e.g., when one machine is a packing machine or when materials have to be transported. Different types of buffers and buffer usage are considered. It is shown that all considered buffer flow shop problems remain NP-hard for the makespan criterion even with the restriction to equal processing times on one machine. However, the special case where the constant c is larger or smaller than all processing times on the other machine is shown to be polynomially solvable by presenting an algorithm (2BF-OPT) that calculates optimal schedules in [Formula: see text] steps. Two heuristics for solving the NP-hard flow shop problems are proposed: i) a modification of the commonly used NEH heuristic (mNEH) and ii) an Iterated Local Search heuristic (2BF-ILS) that uses the mNEH heuristic for computing its initial solution. It is shown experimentally that the proposed 2BF-ILS heuristic obtains better results than two state-of-the-art algorithms for buffered flow shop problems from the literature and an Ant Colony Optimization algorithm. In addition, it is shown experimentally that 2BF-ILS obtains the same solution quality as the standard NEH heuristic, however, with a smaller number of function evaluations.

scholarly journals Oriented Coloring on Recursively Defined Digraphs

Algorithms ◽  
2019 ◽  
Vol 12 (4) ◽  
pp. 87 ◽  
Author(s):  
Frank Gurski ◽  
Dominique Komander ◽  
Carolin Rehs
Keyword(s):  
Chromatic Number ◽  
Linear Time ◽  
Directed Graphs ◽  
Graph Isomorphism ◽  
Oriented Graph ◽  
Time Algorithm ◽  
Isomorphism Problem ◽  
Np Hard ◽  
Graph Isomorphism Problem ◽  
Acyclic Digraph

Coloring is one of the most famous problems in graph theory. The coloring problem on undirected graphs has been well studied, whereas there are very few results for coloring problems on directed graphs. An oriented k-coloring of an oriented graph G = ( V , A ) is a partition of the vertex set V into k independent sets such that all the arcs linking two of these subsets have the same direction. The oriented chromatic number of an oriented graph G is the smallest k such that G allows an oriented k-coloring. Deciding whether an acyclic digraph allows an oriented 4-coloring is NP-hard. It follows that finding the chromatic number of an oriented graph is an NP-hard problem, too. This motivates to consider the problem on oriented co-graphs. After giving several characterizations for this graph class, we show a linear time algorithm which computes an optimal oriented coloring for an oriented co-graph. We further prove how the oriented chromatic number can be computed for the disjoint union and order composition from the oriented chromatic number of the involved oriented co-graphs. It turns out that within oriented co-graphs the oriented chromatic number is equal to the length of a longest oriented path plus one. We also show that the graph isomorphism problem on oriented co-graphs can be solved in linear time.

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