3788531
Degree-Light-Free Graphs and Hamiltonian Cycles
Abstract. Let G and H be graphs. G is said to be degree-light H-free if G is either H-free or, for every induced subgraph K of G with K≅H, and every {u,v}⊆K, distK(u,v)=2 implies max {d(u),d(v)}≥|V(G)|/2. In this paper, we will show that every 2-connected graph with either degree-light {K1,3, P6}-free or degree-light {K1,3, Z}-free is hamiltonian (with three exceptional graphs), where P6 is a path of order 6 and Z is obtained from P6 by adding an edge between the first and the third vertex of P6 (see Figure 1).
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
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
1678832
Code restructuring for improving cache performance of MPSoCs
One of the critical goals in code optimization for MPSoC architectures is to minimize the number of off-chip memory accesses. This is because such accesses can be extremely costly from both performance and power angles. While conventional data locality optimization techniques can be used for improving data access pattern of each processor independently, such techniques usually do not consider locality for shared data. This paper proposes a strategy that reduces the number of off-chip references due to shared data. It achieves this goal by restructuring a parallelized application code in such a fashion that a given data block is accessed by parallel processors within the same time frame, so that its reuse is maximized while it is in the on-chip memory space. This tends to minimize the number of off-chip references since the accesses to a given data block are clustered within a short period of time during execution. Our approach employs a polyhedral tool that helps us isolate computations that manipulate a given data block.
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.
10105488
Energy savings through compression in embedded Java environments
Limited energy and memory resources are important constraints in the design of an embedded system. Compression is a useful and widely employed mechanism to reduce the memory requirements of the system. As the leakage energy of a memory system increases with its size and because of the increasing contribution of leakage to overall system energy, compression also has a significant effect on reducing energy consumption. However, storing compressed data / instructions has a performance and energy overhead associated with decompression at runtime. The underlying compression algorithm, the corresponding implementation of the decompression and the ability to reuse decompressed information critically impact this overhead. In this paper, we explore the influence of compression on overall memory energy using a commercial embedded Java virtual machine (JVM) and a customized compression algorithm. Our results show that compression is effective in reducing energy even when considering the runtime decompression overheads; for most applications.
2166475
Temperature-sensitive loop parallelization for chip multiprocessors
In this paper, we present and evaluate three temperature-sensitive loop parallelization strategies for array-intensive applications executed on chip multiprocessors in order to reduce the peak temperature. Our experimental results show that the peak (average) temperature can be reduced by 20.9/spl deg/C (4.3/spl deg/C) when averaged over all the applications tested, incurring small performance/power penalties.
18026835
Code protection for resource-constrained embedded devices
While the machine neutral Java bytecodes are attractive for code distribution in the highly heterogeneous embedded domain, the well-documented and standardized features also make it difficult to protect these codes. In fact, there are several tools to reverse engineer Java bytecodes. The focus of this work is the design of a substitution-based bytecode obfuscation approach that prevents code from being executed on unauthorized devices. Furthermore, we also improve the resilience of this substitution-based approach to frequency-based attacks. Using various Java class files, we show that our approach is 2.5 to 3 times less computationally intensive as compared to a traditional encryption based approach. Our experiments reveal that the protected class files could not execute on unauthorized clients.