ASP Programs with Groundings of Small Treewidth

Improved square coloring of planar graphs

Densely connected sub-Gaussian linear structural equation model learning via ℓ1- and ℓ2-regularized regressions

An adjacent vertex distinguishing total coloring of a graph G is a proper total coloring of G such that any pair of adjacent vertices have distinct sets of colors. The minimum number of colors needed for an adjacent vertex distinguishing total coloring of G is denoted by $\chi''_{a}(G)$ . In this paper, we characterize completely the adjacent vertex distinguishing total chromatic number of planar graphs G with large maximum degree Δ by showing that if Δ?14, then $\varDelta+1\leq \chi''_{a}(G)\leq \varDelta+2$ , and $\chi''_{a}(G)=\varDelta+2$ if and only if G contains two adjacent vertices of maximum degree.

It is proved that a planar graph with maximum degree Δ ≥ 11 has total (vertex-edge) chromatic number $Delta; + 1. © 1997 John Wiley & Sons, Inc. J Graph Theory 26: 53–59, 1997

Given a simple graph $G$, denote by $\Delta(G)$, $\delta(G)$, and $\chi'(G)$ the maximum degree, the minimum degree, and the chromatic index of $G$, respectively. We say $G$ is $\Delta$-critical if $\chi'(G)=\Delta(G)+1$ and $\chi'(H)\le \Delta(G)$ for every proper subgraph $H$ of $G$, and $G$ is overfull if $|E(G)|>\Delta(G) \lfloor |V(G)|/2 \rfloor$. Since a maximum matching in $G$ can have size at most $\lfloor |V(G)|/2 \rfloor$, it follows that $\chi'(G) = \Delta(G) +1$ if $G$ is overfull. Conversely, let $G$ be a $\Delta$-critical graph. The well known overfull conjecture of Chetwynd and Hilton asserts that $G$ is overfull provided $\Delta(G) > |V(G)|/3$. In this paper, we show that any $\Delta$-critical graph $G$ is overfull if $\Delta(G) - 7\delta(G)/4\ge (3|V(G)|-17)/4$.

Theoretical aspects of equitable partition of networks into sparse modules

It is shown by Luo and Zhao (J Graph Theory 73:469---482, 2013) that an overfull $$\Delta $$Δ-critical graph with n vertices that satisfies $$\Delta \ge \frac{n}{2}$$Δźn2 is Hamiltonian. If Hilton'...

Incidence coloring of Mycielskians with fast algorithm

Cooperative applications represent a class of multi-tasking programs where different tasks execute concurrently according to a producer-consumer pattern. This class of programs is increasingly adopted on multi-core architectures and especially on multimedia mobile devices based on MPSoCs. Indeed, it allows to better exploit the architectural parallelism. However, the run-time efficient usage of memory hierarchies still is mandatory to achieve really good performance. Moreover, when responsiveness and predictability of the application are required, obtaining strict real-time behaviors on these architectures is still an interesting research topic. This work proposes a software mechanism to enhance soft real-time behaviours of cooperative applications. Targeting the Linux kernel, this mechanism enhances its real-time scheduler by introducing the support for cache-aware scheduling. On some architectures, the experiments conducted on a synthetic benchmark allow to observe significant improvements, both on execution predictability and data throughput. Further improvements already under investigation are foreseen to extend the benefits to more architectures. Keywords-Real-Time Scheduling, SMP, Cache-Affinity, Linux, Determinism, Throughput

We consider inhomogeneous Erdős–Rényi graphs. We suppose that the maximal mean degree $d$ satisfies $d\ll\log n$. We characterise the asymptotic behaviour of the $n^{1-o(1)}$ largest eigenvalues of the adjacency matrix and its centred version. We prove that these extreme eigenvalues are governed at first order by the largest degrees and, for the adjacency matrix, by the nonzero eigenvalues of the expectation matrix. Our results show that the extreme eigenvalues exhibit a novel behaviour which in particular rules out their convergence to a nondegenerate point process. Together with the companion paper [Benaych-Georges, Bordenave and Knowles (2017)], where we analyse the extreme eigenvalues in the complementary regime $d\gg\log n$, this establishes a crossover in the behaviour of the extreme eigenvalues around $d\sim\log n$. Our proof relies on a tail estimate for the Poisson approximation of an inhomogeneous sum of independent Bernoulli random variables, as well as on an estimate on the operator norm of a pruned graph due to Le, Levina, and Vershynin from [Random Structures Algorithms 51 (2017) 538–561].

We define and study a perfect \((1,2)\)-dominating set which is a special case of a \((1,2)\)-dominating set. We discuss the existence of a perfect \((1,2)\)-dominating set in graphs with at most two vertices of maximum degree. In particular, we present a complete solution if the maximum degree equals \(n-1\) or \(n-2\).

Hypergraph incidence coloring

Edge-colouring graphs with local list sizes

The Glasgow Haskell Compiler (GHC) is a well supported optimizing compiler for the Haskell programming language, along with its own extensions to the language and libraries. Haskell's lazy semantics imposes a runtime model which is in general difficult to implement efficiently. GHC achieves good performance across a wide variety of programs via aggressive optimization taking advantage of the lack of side effects, and by targeting a carefully tuned virtual machine. The Intel Labs Haskell Research Compiler uses GHC as a frontend, but provides a new whole-program optimizing backend by compiling the GHC intermediate representation to a relatively generic functional language compilation platform. We found that GHC's external Core language was relatively easy to use, but reusing GHC's libraries and achieving full compatibility were harder. For certain classes of programs, our platform provides substantial performance benefits over GHC alone, performing 2x faster than GHC with the LLVM backend on selected modern performance-oriented benchmarks; for other classes of programs, the benefits of GHC's tuned virtual machine continue to outweigh the benefits of more aggressive whole program optimization. Overall we achieve parity with GHC with the LLVM backend. In this paper, we describe our Haskell compiler stack, its implementation and optimization approach, and present benchmark results comparing it to GHC.

The well-founded semantics is one of the most widely studied and used semantics of logic programs with negation. In the case of finite propositional programs, it can be computed in polynomial time, more specifically, in O([mid ]At(P)[mid ] × size(P)) steps, where size(P) denotes the total number of occurrences of atoms in a logic program P. This bound is achieved by an algorithm introduced by Van Gelder and known as the alternating-fixpoint algorithm. Improving on the alternating-fixpoint algorithm turned out to be difficult. In this paper we study extensions and modifications of the alternating-fixpoint approach. We then restrict our attention to the class of programs whose rules have no more than one positive occurrence of an atom in their bodies. For programs in that class we propose a new implementation of the alternating-fixpoint method in which false atoms are computed in a top-down fashion. We show that our algorithm is faster than other known algorithms and that for a wide class of programs it is linear and so, asymptotically optimal.