39660968
A special k-coloring for a connected k-chromatic graph
For each positive integer k we consider the smallest positive integer f(k) (dependent only on k) such that the following holds: Each connected graph G with chromatic number ?(G) = k can be properly vertex colored by k colors so that for each pair of vertices xo and xp in any color class there exist vertices x1, x2, ?, xp-1 of the same class with dist(xi, xi+1) ? f(k) for each i, 0 ? i ? p ? 1. Thus, the graph is k-colorable with the vertices of each color class placed throughout the graph so that no subset of the class is at a distance > f(k) from the remainder of the class.We prove that f(k) < 12k when the order of the graph is ? k(k ? 2) + 1.
9764979
Tough enough chordal graphs are Hamiltonian
3744350
Hamiltonian graphs involving neighborhood unions
Dirac proved that a graph G is hamiltonian if the minimum degree δ(G) ≥ n/2, where n is the order of G. Let G be a graph and A ⊆ V(G). The neighborhood of A is N(A) = {b : ab ∈ E(G) for some a ∈ A}. For any positive integer k, we show that every (2k − 1)-connected graph of order n ≥ 16k is hamiltonian if |N(A)| ≥ n/2 for every independent vertex set A of k vertices. The result contains a few known results as special cases. The case of k = 1 is the classic result of Dirac when n is large and the case of k = 2 is a result of Broersma, Van den Heuvel, and Veldman when n is large. For general k, this result improves a result of Chen and Liu. The lower bound 2k − 1 on connectivity is best possible in general while the lower bound 16k for n is conjectured to be unnecessary. © 2006 Wiley Periodicals, Inc. J Graph Theory 53: 83–100, 2006
43538481
Vertex-disjoint cycles containing specified vertices in a bipartite graph
A minimum degree condition is given for a bipartite graph to contain a 2-factor each component of which contains a previously specified vertex. 2004 Wiley Periodicals, Inc. J Graph Theory 46: 145–166, 2004
1039631
New Conditions for k-ordered Hamiltonian Graphs
We show that in any graph G on n vertices with d(x) + d(y) ≥ n for any two nonadjacent vertices x and y, we can fix the order of k vertices on a given cycle and find a hamiltonian cycle encountering these vertices in the same order, as long as k < n/12 and G is d(k + 1)/2e-connected. Further we show that every b3k/2cconnected graph on n vertices with d(x) + d(y) ≥ n for any two nonadjacent vertices x and y is k-ordered hamiltonian, i.e. for every ordered set of k vertices we can find a hamiltonian cycle encountering these vertices in the given order. Both connectivity bounds are best possible.
3811952
Degree Sequences with Repeated Values
A given nonincreasing sequence D = (d1, d2, · · · , dn) is said to contain a (nonincreasing) repetition sequence D∗ = (di1 , di2 , · · · , dik ) for some k ≤ n − 2 if all values of D −D∗ are distinct and for any dil ∈ D ∗ there exists some dt ∈ D −D∗ such that dil = dt. For any pair of integers n and k with n ≥ k + 2, we investigate the existence of a graphic sequence which contains a given repetition sequence. Our main theorem contains the known results for the special case di1 = dik if k = 1 or k = 2 (see [1, 5, 2]). 1supported in part by a foundation of Academia Sinica.
17088807
Reducing NoC energy consumption through compiler-directed channel voltage scaling
While scalable NoC (Network-on-Chip) based communication architectures have clear advantages over long point-to-point communication channels, their power consumption can be very high. In contrast to most of the existing hardware-based efforts on NoC power optimization, this paper proposes a compiler-directed approach where the compiler decides the appropriate voltage/frequency levels to be used for each communication channel in the NoC. Our approach builds and operates on a novel graph based representation of a parallel program and has been implemented within an optimizing compiler and tested using 12 embedded benchmarks. Our experiments indicate that the proposed approach behaves better - from both performance and power perspectives - than a hardwarebased scheme and the energy savings it achieves are very close to the savings that could be obtained from an optimal, but hypothetical voltage/frequency scaling scheme.
10538824
Parallel Decomposition of Generalized Series-Parallel Graphs
Generalized series-parallel (GSP) graphs belong to the class of decomposable graphs which can be represented by their decomposition trees. Given a decomposition tree of a GSP graph, there are many graph-theoretic problems which can be solved efficiently. An efficient parallel algorithm for constructing a decomposition tree of a given GSP graph is presented. It takes O(log n) time with C(m, n) processors on a CRCW PRAM, where C(m, n) is the number of processors required to find connected components of a graph with in edges and n vertices in logarithmic time. Based on our algorithmic results, we also derive some properties for GSP graphs, which may be of interest in and of themselves.
45776383
Efficient Parallel Algorithms for Doubly Convex-Bipartite Graphs
Suppose that G = (S, T, E) is a bipartite graph. An ordering of S(T) has the adjacency property if for each vertex in T(S), its adjacent vertices in S(T) are consecutive in the ordering. If there exist orderings of S and T which have the adjacency property, G is called a doubly convex-bipartite graph. In this paper, a parallel algorithm is proposed to recognize a doubly convex-bipartite graph. The algorithm runs in O(log n) time using O(n3log n) processors on the CRCW PRAM, or O(log2 n) time using O(n3log2 n) processors on the CREW PRAM.
7347899
Data compression for improving SPM behavior
Scratch-pad memories (SPMs) enable fast access to time-critical data. While prior research studied both static and dynamic SPM management strategies, not being able to keep all hot data (i.e., data with high reuse) in the SPM remains the biggest problem. This paper proposes data compression to increase the number of data blocks that can be kept in the SPM. Our experiments with several embedded applications show that our compression-based SPM management heuristic is very effective and outperforms prior static and dynamic SPM management approaches. We also present an ILP formulation of the problem, and show that the proposed heuristic generates competitive results with those obtained through ILP, while spending much less time in compilation.
1852937
Context-sensitive resource discovery
This paper presents the "Solar" system framework that allows resources to advertise context-sensitive names and for applications to make context-sensitive name queries. The heart of our framework is a small specification language that allows composition of "context-processing operators" to calculate the desired context. Resources use the framework to register names, and applications use the framework to look up context-sensitive name descriptions. The back-end system executes these operators and constantly updates the context values, adjusting advertised names and informing applications about changes. We report experimental results from a prototype, using a modified version of the intentional naming system (INS) as the core directory service.