3759042
Extremal graphs for intersecting cliques
For any two positive integers n?r?1, the well-known Turan Theorem states that there exists a least positive integer ex(n,Kr) such that every graph with n vertices and ex(n,Kr)+1 edges contains a subgraph isomorphic to Kr. We determine the minimum number of edges sufficient for the existence of k cliques with r vertices each intersecting in exactly one common vertex.
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.
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
2501005
Coordinating Multiple Agents via Reinforcement Learning
In this paper, we attempt to use reinforcement learning techniques to solve agent coordination problems in task-oriented environments. The Fuzzy Subjective Task Structure model (FSTS) is presented to model the general agent coordination. We show that an agent coordination problem modeled in FSTS is a Decision-Theoretic Planning (DTP) problem, to which reinforcement learning can be applied. Two learning algorithms, ‘‘coarse-grained’’ and ‘‘fine-grained’’, are proposed to address agents coordination behavior at two different levels. The ‘‘coarse-grained’’ algorithm operates at one level and tackle hard system constraints, and the ‘‘fine-grained’’ at another level and for soft constraints. We argue that it is important to explicitly model and explore coordination-specific (particularly system constraints) information, which underpins the two algorithms and attributes to the effectiveness of the algorithms. The algorithms are formally proved to converge and experimentally shown to be effective.
206570229
Graphs with Linearly Bounded Ramsey Numbers
Abstract A graph G of order n is p -arrangeable if its vertices can be ordered as v 1 , v 2 , ..., v n such that | N L i ( N Ri ( v i ))| ≤ p for each 1 ≤ i ≤ n − 1, where L i = { v 1 , v 2 , ..., v i }, R i = { v i +1 , v i +2 , ..., v n }, and N A ( B ) denotes the neighbors of B which lie in A . We prove that for each p ≥ 1, there is a constant c (depending only on p ) such that the Ramsey number r ( G , G ) ≤ cn for each p -arrangeable graph G of order n . Further we prove that there exists a fixed positive integer p such that all planar graphs are p -arrangeable.
25434953
A data-centric approach to checksum reuse for array-intensive applications
Soft errors are transient faults that occur in VLSI circuits due to external radiation and affect the logic states of sensitive components. While many systems implement hardware-based protection techniques like ECC and other approaches to ensure an acceptable level of robustness against these errors, such solutions are generally very rigid and costly. Recent research discussed checksum-based software solutions that can be used in the context of array-intensive computations. While a checksum-based scheme can be more flexible than a hardware-based approach to reliability, it can also bring significant runtime overheads. Focusing on array-intensive applications, this paper proposes a compiler-directed data-centric strategy that maximizes reuse of checksums. A unique characteristic of the proposed scheme is that it can work with a given checksum assignment, and automatically - under compiler guidance - restructures the entire application code to maximize checksum reuse. This scheme can reduce checksum recomputing even further by inter-procedural checksum reuse. Our experiments clearly show that the proposed approach reduces the number of checksum calculations required by the previous work.
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.
8725655
Optimizing address code generation for array-intensive DSP applications
The application code size is a critical design factor for many embedded systems. Unfortunately, most available compilers optimize primarily for speed of execution rather than code density. As a result, the compiler-generated code can be much larger than necessary. In particular, in the DSP domain, the past research found that optimizing address code generation can be very important since address code can account for over 50% of all program bits. This paper presents a compiler-directed scheme to minimize the number of instructions to be generated to manipulate address registers found in DSP architectures. As opposed to most of the prior techniques that attempt to reduce the number of such instructions through careful address register assignment, this paper proposes modifying loop access patterns in array-intensive signal processing applications. In addition, it demonstrates how the proposed scheme can cooperate with a data layout optimizer for increasing its benefits further. We also discuss how optimizations that target effective address code generation can conflict with data locality-enhancing transformations. We evaluate the proposed approach using twelve array-intensive embedded applications. Our experimental results indicate that the proposed approach not only leads to significant reductions in code size but also outperforms prior efforts on reducing code size of array-intensive DSP applications.