Complexity of coalition structure generation

We revisit the coalition structure generation problem in which the goal is to partition the players into exhaustive and disjoint coalitions so as to maximize the social welfare. One of our key results is a general polynomial-time algorithm to solve the problem for all coalitional games provided that player types are known and the number of player types is bounded by a constant. As a corollary, we obtain a polynomial-time algorithm to compute an optimal partition for weighted voting games with a constant number of weight values and for coalitional skill games with a constant number of skills. We also consider well-studied and well-motivated coalitional games defined compactly on combinatorial domains. For these games, we characterize the complexity of computing an optimal coalition structure by presenting polynomial-time algorithms, approximation algorithms, or NP-hardness and inapproximability lower bounds.Comment: 17 page

Mechanical generation of networks with surplus complexity

In previous work I examined an information based complexity measure of networks with weighted links. The measure was compared with that obtained from by randomly shuffling the original network, forming an Erdos-Renyi random network preserving the original link weight distribution. It was found that real world networks almost invariably had higher complexity than their shuffled counterparts, whereas networks mechanically generated via preferential attachment did not. The same experiment was performed on foodwebs generated by an artificial life system, Tierra, and a couple of evolutionary ecology systems, EcoLab and WebWorld. These latter systems often exhibited the same complexity excess shown by real world networks, suggesting that the complexity surplus indicates the presence of evolutionary dynamics. In this paper, I report on a mechanical network generation system that does produce this complexity surplus. The heart of the idea is to construct the network of state transitions of a chaotic dynamical system, such as the Lorenz equation. This indicates that complexity surplus is a more fundamental trait than that of being an evolutionary system.Comment: Accepted for ACALCI 2015 Newcastle, Australi

Complexity Analysis Of Next-Generation VVC Encoding and Decoding

While the next generation video compression standard, Versatile Video Coding (VVC), provides a superior compression efficiency, its computational complexity dramatically increases. This paper thoroughly analyzes this complexity for both encoder and decoder of VVC Test Model 6, by quantifying the complexity break-down for each coding tool and measuring the complexity and memory requirements for VVC encoding/decoding. These extensive analyses are performed for six video sequences of 720p, 1080p, and 2160p, under Low-Delay (LD), Random-Access (RA), and All-Intra (AI) conditions (a total of 320 encoding/decoding). Results indicate that the VVC encoder and decoder are 5x and 1.5x more complex compared to HEVC in LD, and 31x and 1.8x in AI, respectively. Detailed analysis of coding tools reveals that in LD on average, motion estimation tools with 53%, transformation and quantization with 22%, and entropy coding with 7% dominate the encoding complexity. In decoding, loop filters with 30%, motion compensation with 20%, and entropy decoding with 16%, are the most complex modules. Moreover, the required memory bandwidth for VVC encoding/decoding are measured through memory profiling, which are 30x and 3x of HEVC. The reported results and insights are a guide for future research and implementations of energy-efficient VVC encoder/decoder.Comment: IEEE ICIP 202

Generation of Molecular Complexity from Cyclooctatetraene: Preparation of Aminobicyclo[5.1.0]octitols

A series of eight stereoisomeric N-(tetrahydroxy bicyclo-[5.1.0]oct-2S*-yl)phthalimides were prepared in one to four steps from N-(bicyclo[5.1.0]octa-3,5-dien-2-yl)phthalimide (±)-7, which is readily available from cyclooctatetraene (62 % yield). The structural assignments of the stereoisomers were established by 1H NMR spectral data as well as X-ray crystal structures for certain members. The outcomes of several epoxydiol hydrolyses, particularly ring contraction and enlargement, are of note. The isomeric phthalimides as well as the free amines did not exhibit β-glucosidase inhibitory activity at a concentration of less than 100 μM

Gaussian Entanglement Distribution via Satellite

In this work we analyse three quantum communication schemes for the generation of Gaussian entanglement between two ground stations. Communication occurs via a satellite over two independent atmospheric fading channels dominated by turbulence-induced beam wander. In our first scheme the engineering complexity remains largely on the ground transceivers, with the satellite acting simply as a reflector. Although the channel state information of the two atmospheric channels remains unknown in this scheme, the Gaussian entanglement generation between the ground stations can still be determined. On the ground, distillation and Gaussification procedures can be applied, leading to a refined Gaussian entanglement generation rate between the ground stations. We compare the rates produced by this first scheme with two competing schemes in which quantum complexity is added to the satellite, thereby illustrating the trade-off between space-based engineering complexity and the rate of ground-station entanglement generation.Comment: Closer to published version (to appear in Phys. Rev. A) 13 pages, 6 figure

Mutation of Directed Graphs -- Corresponding Regular Expressions and Complexity of Their Generation

Directed graphs (DG), interpreted as state transition diagrams, are traditionally used to represent finite-state automata (FSA). In the context of formal languages, both FSA and regular expressions (RE) are equivalent in that they accept and generate, respectively, type-3 (regular) languages. Based on our previous work, this paper analyzes effects of graph manipulations on corresponding RE. In this present, starting stage we assume that the DG under consideration contains no cycles. Graph manipulation is performed by deleting or inserting of nodes or arcs. Combined and/or multiple application of these basic operators enable a great variety of transformations of DG (and corresponding RE) that can be seen as mutants of the original DG (and corresponding RE). DG are popular for modeling complex systems; however they easily become intractable if the system under consideration is complex and/or large. In such situations, we propose to switch to corresponding RE in order to benefit from their compact format for modeling and algebraic operations for analysis. The results of the study are of great potential interest to mutation testing

Uniform random sampling of planar graphs in linear time

This article introduces new algorithms for the uniform random generation of labelled planar graphs. Its principles rely on Boltzmann samplers, as recently developed by Duchon, Flajolet, Louchard, and Schaeffer. It combines the Boltzmann framework, a suitable use of rejection, a new combinatorial bijection found by Fusy, Poulalhon and Schaeffer, as well as a precise analytic description of the generating functions counting planar graphs, which was recently obtained by Gim\'enez and Noy. This gives rise to an extremely efficient algorithm for the random generation of planar graphs. There is a preprocessing step of some fixed small cost. Then, the expected time complexity of generation is quadratic for exact-size uniform sampling and linear for approximate-size sampling. This greatly improves on the best previously known time complexity for exact-size uniform sampling of planar graphs with $n$ vertices, which was a little over $O(n^7)$.Comment: 55 page