On the Complexity of an Unregulated Traffic Crossing

The steady development of motor vehicle technology will enable cars of the near future to assume an ever increasing role in the decision making and control of the vehicle itself. In the foreseeable future, cars will have the ability to communicate with one another in order to better coordinate their motion. This motivates a number of interesting algorithmic problems. One of the most challenging aspects of traffic coordination involves traffic intersections. In this paper we consider two formulations of a simple and fundamental geometric optimization problem involving coordinating the motion of vehicles through an intersection. We are given a set of $n$ vehicles in the plane, each modeled as a unit length line segment that moves monotonically, either horizontally or vertically, subject to a maximum speed limit. Each vehicle is described by a start and goal position and a start time and deadline. The question is whether, subject to the speed limit, there exists a collision-free motion plan so that each vehicle travels from its start position to its goal position prior to its deadline. We present three results. We begin by showing that this problem is NP-complete with a reduction from 3-SAT. Second, we consider a constrained version in which cars traveling horizontally can alter their speeds while cars traveling vertically cannot. We present a simple algorithm that solves this problem in $O(n \log n)$ time. Finally, we provide a solution to the discrete version of the problem and prove its asymptotic optimality in terms of the maximum delay of a vehicle

Running Genetic Algorithms in the Edge: A First Analysis

Nowadays, the volume of data produced by different kinds of devices is continuously growing, making even more difficult to solve the many optimization problems that impact directly on our living quality. For instance, Cisco projected that by 2019 the volume of data will reach 507.5 zettabytes per year, and the cloud traffic will quadruple. This is not sustainable in the long term, so it is a need to move part of the intelligence from the cloud to a highly decentralized computing model. Considering this, we propose a ubiquitous intelligent system which is composed by different kinds of endpoint devices such as smartphones, tablets, routers, wearables, and any other CPU powered device. We want to use this to solve tasks useful for smart cities. In this paper, we analyze if these devices are suitable for this purpose and how we have to adapt the optimization algorithms to be efficient using heterogeneous hardware. To do this, we perform a set of experiments in which we measure the speed, memory usage, and battery consumption of these devices for a set of binary and combinatorial problems. Our conclusions reveal the strong and weak features of each device to run future algorihms in the border of the cyber-physical system.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. This research has been partially funded by the Spanish MINECO and FEDER projects TIN2014-57341-R (http://moveon.lcc.uma.es), TIN2016-81766-REDT (http://cirti.es), TIN2017-88213-R (http://6city.lcc.uma.es), the Ministry of Education of Spain (FPU16/02595

b-coloring is NP-hard on co-bipartite graphs and polytime solvable on tree-cographs

A b-coloring of a graph is a proper coloring such that every color class contains a vertex that is adjacent to all other color classes. The b-chromatic number of a graph G, denoted by \chi_b(G), is the maximum number t such that G admits a b-coloring with t colors. A graph G is called b-continuous if it admits a b-coloring with t colors, for every t = \chi(G),\ldots,\chi_b(G), and b-monotonic if \chi_b(H_1) \geq \chi_b(H_2) for every induced subgraph H_1 of G, and every induced subgraph H_2 of H_1. We investigate the b-chromatic number of graphs with stability number two. These are exactly the complements of triangle-free graphs, thus including all complements of bipartite graphs. The main results of this work are the following: - We characterize the b-colorings of a graph with stability number two in terms of matchings with no augmenting paths of length one or three. We derive that graphs with stability number two are b-continuous and b-monotonic. - We prove that it is NP-complete to decide whether the b-chromatic number of co-bipartite graph is at most a given threshold. - We describe a polynomial time dynamic programming algorithm to compute the b-chromatic number of co-trees. - Extending several previous results, we show that there is a polynomial time dynamic programming algorithm for computing the b-chromatic number of tree-cographs. Moreover, we show that tree-cographs are b-continuous and b-monotonic

The impact of using combinatorial optimisation for static caching of posting lists

Abstract. Caching posting lists can reduce the amount of disk I/O required to evaluate a query. Current methods use optimisation proce-dures for maximising the cache hit ratio. A recent method selects posting lists for static caching in a greedy manner and obtains higher hit rates than standard cache eviction policies such as LRU and LFU. However, a greedy method does not formally guarantee an optimal solution. We investigate whether the use of methods guaranteed, in theory, to find an approximately optimal solution would yield higher hit rates. Thus, we cast the selection of posting lists for caching as an integer linear pro-gramming problem and perform a series of experiments using heuristics from combinatorial optimisation (CCO) to find optimal solutions. Using simulated query logs we find that CCO yields comparable results to a greedy baseline using cache sizes between 200 and 1000 MB, with modest improvements for queries of length two to three

Proof Theory and Ordered Groups

Ordering theorems, characterizing when partial orders of a group extend to total orders, are used to generate hypersequent calculi for varieties of lattice-ordered groups (l-groups). These calculi are then used to provide new proofs of theorems arising in the theory of ordered groups. More precisely: an analytic calculus for abelian l-groups is generated using an ordering theorem for abelian groups; a calculus is generated for l-groups and new decidability proofs are obtained for the equational theory of this variety and extending finite subsets of free groups to right orders; and a calculus for representable l-groups is generated and a new proof is obtained that free groups are orderable

Necessary and sufficient conditions of solution uniqueness in ℓ1\ell_1 minimization

This paper shows that the solutions to various convex $\ell_1$ minimization problems are \emph{unique} if and only if a common set of conditions are satisfied. This result applies broadly to the basis pursuit model, basis pursuit denoising model, Lasso model, as well as other $\ell_1$ models that either minimize $f(Ax-b)$ or impose the constraint $f(Ax-b)\leq\sigma$, where $f$ is a strictly convex function. For these models, this paper proves that, given a solution $x^*$ and defining I=\supp(x^*) and s=\sign(x^*_I), $x^*$ is the unique solution if and only if $A_I$ has full column rank and there exists $y$ such that $A_I^Ty=s$ and $|a_i^Ty|_\infty<1$ for $i\not\in I$. This condition is previously known to be sufficient for the basis pursuit model to have a unique solution supported on $I$. Indeed, it is also necessary, and applies to a variety of other $\ell_1$ models. The paper also discusses ways to recognize unique solutions and verify the uniqueness conditions numerically.Comment: 6 pages; revised version; submitte

Characterizing the universal rigidity of generic frameworks

A framework is a graph and a map from its vertices to E^d (for some d). A framework is universally rigid if any framework in any dimension with the same graph and edge lengths is a Euclidean image of it. We show that a generic universally rigid framework has a positive semi-definite stress matrix of maximal rank. Connelly showed that the existence of such a positive semi-definite stress matrix is sufficient for universal rigidity, so this provides a characterization of universal rigidity for generic frameworks. We also extend our argument to give a new result on the genericity of strict complementarity in semidefinite programming.Comment: 18 pages, v2: updates throughout; v3: published versio

Removing exogenous information using pedigree data

Management of certain populations requires the preservation of its pure genetic background. When, for different reasons, undesired alleles are introduced, the original genetic conformation must be recovered. The present study tested, through computer simulations, the power of recovery (the ability for removing the foreign information) from genealogical data. Simulated scenarios comprised different numbers of exogenous individuals taking partofthe founder population anddifferent numbers of unmanaged generations before the removal program started. Strategies were based on variables arising from classical pedigree analyses such as founders? contribution and partial coancestry. The ef?ciency of the different strategies was measured as the proportion of native genetic information remaining in the population. Consequences on the inbreeding and coancestry levels of the population were also evaluated. Minimisation of the exogenous founders? contributions was the most powerful method, removing the largest amount of genetic information in just one generation.However, as a side effect, it led to the highest values of inbreeding. Scenarios with a large amount of initial exogenous alleles (i.e. high percentage of non native founders), or many generations of mixing became very dif?cult to recover, pointing out the importance of being careful about introgression events in populatio

Generating Computational Models for Serious Gaming

Westera, W. (2013, 25 October). Generating computational models for serious gaming. Presentation at the GALA Serious Gaming Conference, Paris, France.Many serious games include computational models that simulate dynamic systems. These models promote enhanced interaction and responsiveness. Under the social web paradigm more and more usable game authoring tools become available that enable prosumers to create their own games, but the inclusion of dynamic simulations remains a specialist’s job involving knowledge of mathematics, numerical modeling and programming. This presentation explains a methodology for specifying and running a specific subset of computational models without the need of bothering with mathematical equations. The methodology comprises a knowledge elicitation procedure for identifying and specifying the required model components, whereupon the mathematical model is automatically generated. The approach is based on the fact that many games focus on optimisation problems that are covered by a general class of linear programming models. The presentation thus sketches the principles of a creativity tool that removes barriers for harvesting the creative potential of teachers and students