23991617
Ramsey Problems With Bounded Degree Spread
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
9764979
Tough enough chordal graphs are Hamiltonian
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.
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
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.
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.
40869256
Parallel algorithms for permutation graphs
In this paper, parallel algorithms are presented for solving some problems on permutation graphs. The coloring problem is solved inO(log2n) time usingO(n3/logn) processors on the CREW PRAM, orO(logn) time usingO(n3) processors on the CRCW PRAM. The weighted clique problem, the weighted independent set problem, the cliques cover problem, and the maximal layers problem are all solved with the same complexities. We can also show that the longest common subsequence problem belongs to the class NC.
17483991
Energy-aware computation duplication for improving reliability in embedded chip multiprocessors
Compilers designed for current embedded systems must be capable of addressing multiple constraints such as low power, high performance, small memory footprint and form factor, and high reliability at the same time. In particular, optimizing for one constraint should be performed carefully, considering its impact on other constraints. Recent trends indicate that transient errors are becoming increasingly important in embedded systems. Focusing on an embedded chip multiprocessor and array-intensive applications, this paper demonstrates how reliability against transient errors can be improved without impacting execution time by utilizing idle processors for duplicating some of the computations of the active processors. It also shows how a balance between power savings and reliability improvement can be struck using a metric called the energy-delay-fallibility product. Our experimental results indicate that the "percentage of duplicated computations" is a useful high-level metric for studying the tradeoffs among performance, power, and reliability
1466511
Activity Clustering for Leakage Management in SPMs
This paper proposes compiler-based leakage optimization strategy for on-chip scratch-pad memories (SPMs). The idea is to keep only a small set of SPM regions active at a given time and pre-activate SPM regions based on the compiler-extracted data access pattern. Our strategy, called activity clustering, increases the length of the idle periods of SPM regions by clustering accesses to a small set of regions at a time. It thus allows an SPM to take better advantage of the underlying leakage optimization mechanism
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.