scholarly journals Algorithms for Manipulating Sequential Allocation

2020 ◽  
Vol 34 (02) ◽  
pp. 2302-2309
Author(s):  
Mingyu Xiao ◽  
Jiaxing Ling
Keyword(s):  
Computational Complexity ◽  
Open Problem ◽  
Arbitrary Number ◽  
Fixed Number ◽  
Preference Ranking ◽  
Best Response ◽  
Sequential Allocation ◽  
Np Complete ◽  
Polynomially Solvable ◽  
Novel Algorithm

Sequential allocation is a simple and widely studied mechanism to allocate indivisible items in turns to agents according to a pre-specified picking sequence of agents. At each turn, the current agent in the picking sequence picks its most preferred item among all items having not been allocated yet. This problem is well-known to be not strategyproof, i.e., an agent may get more utility by reporting an untruthful preference ranking of items. It arises the problem: how to find the best response of an agent? It is known that this problem is polynomially solvable for only two agents and NP-complete for an arbitrary number of agents. The computational complexity of this problem with three agents was left as an open problem. In this paper, we give a novel algorithm that solves the problem in polynomial time for each fixed number of agents. We also show that an agent can always get at least half of its optimal utility by simply using its truthful preference as the response.

The computational complexity of graph contractions I: Polynomially solvable and NP-complete cases

Networks ◽  
2007 ◽  
Vol 51 (3) ◽  
pp. 178-189 ◽  
Author(s):  
Asaf Levin ◽  
Daniel Paulusma ◽  
Gerhard J. Woeginger
Keyword(s):  
Computational Complexity ◽  
Np Complete ◽  
Polynomially Solvable

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.

scholarly journals Popular Matching in Roommates Setting Is NP-hard

2021 ◽  
Vol 13 (2) ◽  
pp. 1-20
Author(s):  
Sushmita Gupta ◽  
Pranabendu Misra ◽  
Saket Saurabh ◽  
Meirav Zehavi
Keyword(s):  
Computational Complexity ◽  
Np Hard ◽  
Np Complete ◽  
Open Question ◽  
Popular Matching

An input to the P OPULAR M ATCHING problem, in the roommates setting (as opposed to the marriage setting), consists of a graph G (not necessarily bipartite) where each vertex ranks its neighbors in strict order, known as its preference. In the P OPULAR M ATCHING problem the objective is to test whether there exists a matching M * such that there is no matching M where more vertices prefer their matched status in M (in terms of their preferences) over their matched status in M *. In this article, we settle the computational complexity of the P OPULAR M ATCHING problem in the roommates setting by showing that the problem is NP-complete. Thus, we resolve an open question that has been repeatedly and explicitly asked over the last decade.

scholarly journals Iterative inversion algorithm for an interference correlation matrix

2017 ◽  
pp. 4-9
Author(s):  
A. V. Yastrebov
Keyword(s):  
Computational Complexity ◽  
Correlation Matrix ◽  
Fixed Number ◽  
Inversion Algorithm ◽  
Weight Factors ◽  
Channel Interference ◽  
Iterative Inversion ◽  
Interference Canceller

The article considers efficiency of a multi-channel interference canceller as a function of the number of compensation channels used for a fixed number of jammers. The author suggests an iterative inversion algorithm for an interference correlation matrix, making it possible to achieve zero loss at a certain stage and decrease the computational complexity of determining weight factors for compensation channels

THE HOSOYA INDEX OF GRAPHS FORMED BY A FRACTAL GRAPH

Fractals ◽  
2019 ◽  
Vol 27 (08) ◽  
pp. 1950135 ◽  
Author(s):  
JIA-BAO LIU ◽  
JING ZHAO ◽  
JIE MIN ◽  
JINDE CAO
Keyword(s):  
Computational Complexity ◽  
Hosoya Index ◽  
Initial Graph ◽  
Np Complete

The computational complexity of the Hosoya index of a given graph is NP-Complete. Let [Formula: see text] be the graph constructed from [Formula: see text] by a triangle instead of all vertices of the initial graph [Formula: see text]. In this paper, we characterize the Hosoya index of the graph [Formula: see text]. To our surprise, it shows that the Hosoya index of [Formula: see text] is thoroughly given by the order and degrees of all the vertices of the initial graph [Formula: see text].

scholarly journals Stable roommates with narcissistic, single-peaked, and single-crossing preferences

2020 ◽  
Vol 34 (2) ◽  
Author(s):  
Robert Bredereck ◽  
Jiehua Chen ◽  
Ugo Paavo Finnendahl ◽  
Rolf Niedermeier
Keyword(s):  
Computational Complexity ◽  
Structural Property ◽  
Incomplete Preferences ◽  
Two Agents ◽  
Single Crossing ◽  
Np Complete

Abstract The classical Stable Roommates problem is to decide whether there exists a matching of an even number of agents such that no two agents which are not matched to each other would prefer to be with each other rather than with their respectively assigned partners. We investigate Stable Roommates with complete (i.e., every agent can be matched with any other agent) or incomplete preferences, with ties (i.e., two agents are considered of equal value to some agent) or without ties. It is known that in general allowing ties makes the problem NP-complete. We provide algorithms for Stable Roommates that are, compared to those in the literature, more efficient when the input preferences are complete and have some structural property, such as being narcissistic, single-peaked, and single-crossing. However, when the preferences are incomplete and have ties, we show that being single-peaked and single-crossing does not reduce the computational complexity—Stable Roommates remains NP-complete.

scholarly journals Spectral Processing for Denoising and Compression of 3D Meshes Using Dynamic Orthogonal Iterations

2020 ◽  
Vol 6 (6) ◽  
pp. 55
Author(s):  
Gerasimos Arvanitis ◽  
Aris S. Lalos ◽  
Konstantinos Moustakas
Keyword(s):  
Computational Complexity ◽  
Laplacian Matrix ◽  
3D Models ◽  
Graph Laplacian ◽  
Fixed Number ◽  
Spectral Processing ◽  
Reconstruction Quality ◽  
And Performance ◽  
Optimal Subspace

Recently, spectral methods have been extensively used in the processing of 3D meshes. They usually take advantage of some unique properties that the eigenvalues and the eigenvectors of the decomposed Laplacian matrix have. However, despite their superior behavior and performance, they suffer from computational complexity, especially while the number of vertices of the model increases. In this work, we suggest the use of a fast and efficient spectral processing approach applied to dense static and dynamic 3D meshes, which can be ideally suited for real-time denoising and compression applications. To increase the computational efficiency of the method, we exploit potential spectral coherence between adjacent parts of a mesh and then we apply an orthogonal iteration approach for the tracking of the graph Laplacian eigenspaces. Additionally, we present a dynamic version that automatically identifies the optimal subspace size that satisfies a given reconstruction quality threshold. In this way, we overcome the problem of the perceptual distortions, due to the fixed number of subspace sizes that is used for all the separated parts individually. Extensive simulations carried out using different 3D models in different use cases (i.e., compression and denoising), showed that the proposed approach is very fast, especially in comparison with the SVD based spectral processing approaches, while at the same time the quality of the reconstructed models is of similar or even better reconstruction quality. The experimental analysis also showed that the proposed approach could also be used by other denoising methods as a preprocessing step, in order to optimize the reconstruction quality of their results and decrease their computational complexity since they need fewer iterations to converge.

LEARNING IN BAYESIAN GAMES BY BOUNDED RATIONAL PLAYERS II: NONMYOPIA

1998 ◽  
Vol 2 (2) ◽  
pp. 141-155 ◽  
Author(s):  
Konstantinos Serfes ◽  
Nicholas C. Yannelis
Keyword(s):  
Nash Equilibrium ◽  
Arbitrary Number ◽  
Bayesian Learning ◽  
Full Information ◽  
Bayesian Games ◽  
Response Strategies ◽  
Bayesian Nash Equilibrium ◽  
Current Period ◽  
Best Response ◽  
Rational Players

We generalize results of earlier work on learning in Bayesian games by allowing players to make decisions in a nonmyopic fashion. In particular, we address the issue of nonmyopic Bayesian learning with an arbitrary number of bounded rational players, i.e., players who choose approximate best-response strategies for the entire horizon (rather than the current period). We show that, by repetition, nonmyopic bounded rational players can reach a limit full-information nonmyopic Bayesian Nash equilibrium (NBNE) strategy. The converse is also proved: Given a limit full-information NBNE strategy, one can find a sequence of nonmyopic bounded rational plays that converges to that strategy.

scholarly journals Computing the Interleaving Distance is NP-Hard

2019 ◽  
Vol 20 (5) ◽  
pp. 1237-1271 ◽  
Author(s):  
Håvard Bakke Bjerkevik ◽  
Magnus Bakke Botnan ◽  
Michael Kerber
Keyword(s):  
Computational Complexity ◽  
Complete Characterization ◽  
Np Hard ◽  
Slight Improvement ◽  
Approximation Factor ◽  
Distance Computation ◽  
Persistence Modules ◽  
Np Complete ◽  
Interleaving Distance

Abstract We show that computing the interleaving distance between two multi-graded persistence modules is NP-hard. More precisely, we show that deciding whether two modules are 1-interleaved is NP-complete, already for bigraded, interval decomposable modules. Our proof is based on previous work showing that a constrained matrix invertibility problem can be reduced to the interleaving distance computation of a special type of persistence modules. We show that this matrix invertibility problem is NP-complete. We also give a slight improvement in the above reduction, showing that also the approximation of the interleaving distance is NP-hard for any approximation factor smaller than 3. Additionally, we obtain corresponding hardness results for the case that the modules are indecomposable, and in the setting of one-sided stability. Furthermore, we show that checking for injections (resp. surjections) between persistence modules is NP-hard. In conjunction with earlier results from computational algebra this gives a complete characterization of the computational complexity of one-sided stability. Lastly, we show that it is in general NP-hard to approximate distances induced by noise systems within a factor of 2.

scholarly journals An evolutionary approach to solve the dynamic multihop ridematching problem

SIMULATION ◽  
2016 ◽  
Vol 93 (1) ◽  
pp. 3-19 ◽  
Author(s):  
Sondes Ben Cheikh ◽  
Christian Tahon ◽  
Slim Hammadi
Keyword(s):  
Arbitrary Number ◽  
Experimental Results ◽  
Time Constraints ◽  
Evolutionary Approach ◽  
Genetic Operators ◽  
Novel Approach ◽  
Np Complete ◽  
Original Dynamic

The multihop ridesharing system generates a ridematching solution with an arbitrary number of transfers that respects personal preferences of the users and their time constraints with detour willingness. As it is considered to be NP-complete, an efficient metaheuristic is required in the application to solve the dynamic multihop ridematching problem. In this context, a novel approach, called Metaheuristics Approach Based on Controlled Genetic Operators ( MACGeO), which is supported by an original dynamic coding, is developed to address the multihop ridematching problem. The performance of the proposed approach is measured via simulation scenarios, which feature various numbers of carpool drivers (vehicles) and riders (passengers). Experimental results show that the multihop ridematching could greatly increase the number of matched requests while minimizing the number of vehicles required.

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