12008114
Weak Clique-Covering Cycles and Paths
In this paper, we investigate the sufficient conditions for a graph to contain a cycle (path) C such that G − V (C) is a disjoint union of cliques. In particular, sufficient conditions involving degree sum and neighborhood union are obtained.
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.
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.
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
9764979
Tough enough chordal graphs are Hamiltonian
17981801
Studying storage-recomputation tradeoffs in memory-constrained embedded processing
Fueled by an unprecedented desire for convenience and self-service, consumers are embracing embedded technology solutions that enhance their mobile lifestyles. Consequently, we witness an unprecedented proliferation of embedded/mobile applications. Most of the environments that execute these applications have severe power, performance, and memory space constraints that need to be accounted for. In particular, memory limitations can present serious challenges to embedded software designers. The current solutions to this problem include sophisticated packaging techniques and code optimizations for effective memory utilization. While the first solution is not scalable, the second one is restricted by intrinsic data dependences in the code that prevent code restructuring. In this paper, we explore an alternate approach for reducing memory space requirements of embedded applications. The idea is to re-compute the result of a code block (potentially multiple times) instead of storing it in memory and performing a memory operation whenever needed. The main benefit of this approach is that it reduces memory space requirements, that is, no memory space is reserved for storing the result of the code block in question.
35779178
On the Quickest Path Problem
In this paper, we propose an O(mn2) time algorithm that finds all-pairs quickest paths in a given network N, where n and m are the numbers of nodes and arcs, respectively, in N. Besides, the quickest path between any two nodes can be determined in O(log m) time, provided O(mn2) time preprocessing is made.
17147705
Distributed algorithms for the quickest path problem
Let N = (V, A, C, L) be a network with node set V, arc set A, positive arc capacity function C, and nonnegative arc lead time function L. The quickest path problems is to find paths in N to transmit a given amount of data such that the transmission time is minimized. In this paper, distributed algorithms are developed for the quickest path problem in an asynchronous communication network. For the one-source quickest path problem, we present three algorithms that require O(rn2) messages and O(2) time, O(n) messages and O(rn) time, and O1+elog w) messages and O(rn1+elog w) time for any e, 0<e<1, respectively, where m = |A|, n = |V|, r is the number of distinct capacity values of N, and w is the maxima arc weight of N. For the all-pairs quickest path problem, we present an algorithm that requires O(mn) messages and O(m) time.
9441131
Exposing disk layout to compiler for reducing energy consumption of parallel disk based systems
Disk subsystem is known to be a major contributor to overall power consumption of high-end parallel systems. Past research proposed several architectural level techniques to reduce disk power by taking advantage of idle periods experienced by disks. While such techniques have been known to be effective in certain cases, they share a common drawback: they operate in a reactive manner; i.e., they control disk power by observing past disk activity (e.g., idle and active periods) and estimating future ones. Consequently, they can miss opportunities for saving power and incur significant performance penalties, due to inaccuracies in predicting idle and active times. Motivated by this observation, this paper proposes and evaluates a compiler-driven approach to reducing disk power consumption of array-based scientific applications executing on parallel architectures. The proposed approach exposes disk layout information to the compiler, allowing it to derive disk access pattern, i.e., the order in which parallel disks are accessed. This paper demonstrates two uses of this information. First, we can do proactive disk power management, i.e., we can select the most appropriate power-saving strategy and disk preactivation strategy based on the compiler-predicted future idle and active periods of parallel disks. Second, we can restructure the application code to increase length of idle periods, which leads to better exploitation of available power-saving capabilities. We implemented both these approaches within an optimizing compiler and tested their effectiveness using a set of benchmark codes from the Spec2000 suite and a disk power simulator. Our results show that the compiler-driven disk power management is very promising. The experimental results also reveal that, while proactive disk power management is very effective, code restructuring for disk power achieves the best energy savings across all the benchmarks tested.
53236604
Compiling for memory emergency