LP-based Covering Games with Low Price of Anarchy

We present a new class of vertex cover and set cover games. The price of anarchy bounds match the best known constant factor approximation guarantees for the centralized optimization problems for linear and also for submodular costs -- in contrast to all previously studied covering games, where the price of anarchy cannot be bounded by a constant (e.g. [6, 7, 11, 5, 2]). In particular, we describe a vertex cover game with a price of anarchy of 2. The rules of the games capture the structure of the linear programming relaxations of the underlying optimization problems, and our bounds are established by analyzing these relaxations. Furthermore, for linear costs we exhibit linear time best response dynamics that converge to these almost optimal Nash equilibria. These dynamics mimic the classical greedy approximation algorithm of Bar-Yehuda and Even [3]

Price Linkages of Russian Regional Markets

Exploiting time series of the cost of a staples basket across 75 Russian regions over 1994-2000, price linkages of the regions are analyzed with the use of Granger causality as a tool. Price linkages of Russian regions are found extensive: on average, an individual regional market is linked through prices with 62% of others. Neither isolated clusters of regions nor autarkic regions are revealed; each region is linked with all others either directly or indirectly, through a chain of no more than two intermediate regions. Spatial autocorrelation is found to be widespread, taking place in two thirds of regions.http://deepblue.lib.umich.edu/bitstream/2027.42/57219/1/wp839 .pd

Distance-generalized Core Decomposition

The $k$-core of a graph is defined as the maximal subgraph in which every vertex is connected to at least $k$ other vertices within that subgraph. In this work we introduce a distance-based generalization of the notion of $k$-core, which we refer to as the $(k,h)$-core, i.e., the maximal subgraph in which every vertex has at least $k$ other vertices at distance $\leq h$ within that subgraph. We study the properties of the $(k,h)$-core showing that it preserves many of the nice features of the classic core decomposition (e.g., its connection with the notion of distance-generalized chromatic number) and it preserves its usefulness to speed-up or approximate distance-generalized notions of dense structures, such as $h$-club. Computing the distance-generalized core decomposition over large networks is intrinsically complex. However, by exploiting clever upper and lower bounds we can partition the computation in a set of totally independent subcomputations, opening the door to top-down exploration and to multithreading, and thus achieving an efficient algorithm

Decompositions of edge-colored infinite complete graphs into monochromatic paths

An $r$-edge coloring of a graph or hypergraph $G=(V,E)$ is a map $c:E\to \{0, \dots, r-1\}$. Extending results of Rado and answering questions of Rado, Gy\'arf\'as and S\'ark\"ozy we prove that (1.) the vertex set of every $r$-edge colored countably infinite complete $k$-uniform hypergraph can be partitioned into $r$ monochromatic tight paths with distinct colors (a tight path in a $k$-uniform hypergraph is a sequence of distinct vertices such that every set of $k$ consecutive vertices forms an edge), (2.) for all natural numbers $r$ and $k$ there is a natural number $M$ such that the vertex set of every $r$-edge colored countably infinite complete graph can be partitioned into $M$ monochromatic $k^{th}$ powers of paths apart from a finite set (a $k^{th}$ power of a path is a sequence $v_0, v_1, \dots$ of distinct vertices such that $1\le|i-j| \le k$ implies that $v_iv_j$ is an edge), (3.) the vertex set of every $2$-edge colored countably infinite complete graph can be partitioned into $4$ monochromatic squares of paths, but not necessarily into $3$, (4.) the vertex set of every $2$-edge colored complete graph on $\omega_1$ can be partitioned into $2$ monochromatic paths with distinct colors

Price Linkages of Russian Regional Markets

Exploiting time series of the cost of a staples basket across 75 Russian regions over 1994-2000, price linkages of the regions are analyzed with the use of Granger causality as a tool. Price linkages of Russian regions are found extensive: on average, an individual regional market is linked through prices with 62% of others. Neither isolated clusters of regions nor autarkic regions are revealed; each region is linked with all others either directly or indirectly, through a chain of no more than two intermediate regions. Spatial autocorrelation is found to be widespread, taking place in two thirds of regions.market integration, Granger causality, integration clubs, spatial autocorrelation

A genetic algorithm

Castelli, M., Dondi, R., Manzoni, S., Mauri, G., & Zoppis, I. (2019). Top k 2-clubs in a network: A genetic algorithm. In J. J. Dongarra, J. M. F. Rodrigues, P. J. S. Cardoso, J. Monteiro, R. Lam, V. V. Krzhizhanovskaya, M. H. Lees, ... P. M. A. Sloot (Eds.), Computational Science. ICCS 2019: 19th International Conference, 2019, Proceedings (Vol. 5, pp. 656-663). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11540 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-22750-0_63The identification of cohesive communities (dense sub-graphs) is a typical task applied to the analysis of social and biological networks. Different definitions of communities have been adopted for particular occurrences. One of these, the 2-club (dense subgraphs with diameter value at most of length 2) has been revealed of interest for applications and theoretical studies. Unfortunately, the identification of 2-clubs is a computationally intractable problem, and the search of approximate solutions (at a reasonable time) is therefore fundamental in many practical areas. In this article, we present a genetic algorithm based heuristic to compute a collection of Top k 2-clubs, i.e., a set composed by the largest k 2-clubs which cover an input graph. In particular, we discuss some preliminary results for synthetic data obtained by sampling Erdös-Rényi random graphs.authorsversionpublishe