We study the on-line Steiner tree problem on a general metric space. We show that the greedy on-line algorithm is O(log((d/z)s))-competitive, where s is the number of regular nodes, d is the maximum metric distance be...
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We study the on-line Steiner tree problem on a general metric space. We show that the greedy on-line algorithm is O(log((d/z)s))-competitive, where s is the number of regular nodes, d is the maximum metric distance between any two revealed nodes, and z is the optimal off-line cost. Our results refine the previous known bound [9] and show that algorithm SE of Bartal et al. [3] for the on-line file allocation problem is O(log log N)-competitive on an N-node hypercube or butterfly network. A lower bound of Omega(log((d/z)s)) is shown to hold. We further consider the on-line generalized Steiner problem on a general metric space. We show that a class of lazy and greedy deterministic on-line algorithms are O(root k . log k)-competitive and no on-line algorithm is better than Omega(log k)-competitive, where k is the number of distinct nodes that appear in the request sequence. For the on-line Steiner problem on a directed graph, it is shown that no deterministic on-line algorithm is better than s-competitive and the greedy on-line algorithm is s-competitive.
We consider the progress of the greedy vertex coloring algorithm applied to cycle graphs. In particular we study the asymptotic distribution of the number of vertices colored by the algorith when the third color is fi...
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We consider the progress of the greedy vertex coloring algorithm applied to cycle graphs. In particular we study the asymptotic distribution of the number of vertices colored by the algorith when the third color is first used (if it is). (C) 1995 John Wiley & Sons, Inc.
In a graph, a clique is a set of vertices such that every pair is connected by an edge. MAX-CLIQUE is the optimization problem of finding the largest clique in a given graph and is NP-hard, even to approximate well. S...
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In a graph, a clique is a set of vertices such that every pair is connected by an edge. MAX-CLIQUE is the optimization problem of finding the largest clique in a given graph and is NP-hard, even to approximate well. Several real-world and theory problems can be modeled as MAX-CLIQUE. In this paper, we efficiently approximate MAX-CLIQUE in a special case of the Hopfield network whose stable states are maximal cliques. We present several energy-descent optimizing dynamics;both discrete (deterministic and stochastic) and continuous. One of these emulates, as special cases, two well-known greedy algorithms for approximating MAX-CLIQUE. We report on detailed empirical comparisons on random graphs and on harder ones. Mean-held annealing, an efficient approximation to simulated annealing, and a stochastic dynamics are the narrow but clear winners. All dynamics approximate much better than one which emulates a ''naive'' greedy heuristic.
The matching of line segments between input and prototype characters can be formulated as bipartite weighted matching problem. Under the assumption that the distance of the two line segments and the unmatched penalty ...
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The matching of line segments between input and prototype characters can be formulated as bipartite weighted matching problem. Under the assumption that the distance of the two line segments and the unmatched penalty of any line segment are given, the matching goal is to find a matching such that the sum of the weights of matching edges and the penalties of unmatched vertices is minimum. In this paper, the Hungarian method is applied to solve the matching problem by a reduction algorithm. Moreover, a greedy algorithm based on the Hungarian method is proposed by restricting the above matching which satisfies the constraints of geometric relation. For each iteration in the greedy algorithm, a matched pair is deleted if the relation of their neighbors does not match and a new matching is then found by applying Hungarian method. Finally, we can find a stable matching that preserves the geometric relation. We have implemented this method to recognize on-line Chinese handwritten characters permitting both stroke-order variation and stroke-number variation and a 91% recognition rate is attained.
An optimal on-line algorithm is presented for the following optimization problem, which constitutes the special case of the k-track assignment problem with identical time windows. Intervals arrive at times t(i) and de...
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An optimal on-line algorithm is presented for the following optimization problem, which constitutes the special case of the k-track assignment problem with identical time windows. Intervals arrive at times t(i) and demand service time equal to their length. An interval is considered lost if it is not assigned to one of k identical service stations immediately or if its service is interrupted. Minimizing the losses amounts to coloring a maximal set of intervals in the associated interval graph properly with at most k colors. Optimality of the on-line algorithm is proved by showing that it performs as well as the optimal greedy k-coloring algorithm due to Faigle and Nawijn and, independently, to Carlisle and Lloyd for the same problem under full a priori information.
A real-time algorithm for the (n(2) - 1)-puzzle is designed using greedy and divide-and-conquer techniques. It is proved that (ignoring lower order terms) the new algorithm uses at most 5n(3) moves, and that any such ...
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A real-time algorithm for the (n(2) - 1)-puzzle is designed using greedy and divide-and-conquer techniques. It is proved that (ignoring lower order terms) the new algorithm uses at most 5n(3) moves, and that any such algorithm must make at least n(3) moves in the worst case, at least 2n(3)/3 moves on average, and with probability one, at least 0.264n(3) moves on random configurations.
For a graph H, let Forb(H) be the class of graphs that do not induce H, and let P-5 be the path on five vertices. In this article, we answer two questions of Gyarfas and Lehel. First, we show that there exists a funct...
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For a graph H, let Forb(H) be the class of graphs that do not induce H, and let P-5 be the path on five vertices. In this article, we answer two questions of Gyarfas and Lehel. First, we show that there exists a function f(omega) such that for any graph G is an element of Forb(P-5), the on-line coloring algorithm First-Fit uses at most f(omega(G)) colors on G, where omega(G) is the clique size of G. Second, we show that there exists an on-line algorithm A that will color any graph G is an element of Forb(P-5) with a number of colors exponential in omega(G). Finally, we extend some of our results to larger classes of graphs defined in terms of a list of forbidden subgraphs.
Let G = (V,E) be an n-vertex connected graph with positive edge weights. A subgraph G' = (V, E') is a t-spanner of G if for all u, v is an element of V, the weighted distance between u and v in G' is at mo...
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ISBN:
(纸本)9780897915175
Let G = (V,E) be an n-vertex connected graph with positive edge weights. A subgraph G' = (V, E') is a t-spanner of G if for all u, v is an element of V, the weighted distance between u and v in G' is at most t times the weighted distance between u and v in G. We consider the problem of constructing sparse spanners. Sparseness of spanners is measured by two criteria, the size, defined as the number of edges in the spanner, and the weight, defined as the sum of the edge weights in the spanner. In this paper, we concentrate on constructing spanners of small weight. For an arbitrary positive edge-weighted graph G, for any t > 1, and any epsilon > 0, we show that a t-spanner of G with weight O(n(2+epsilon/t-1)). wt(MST) can be constructed in polynomial time. We also show that (log(2) n)-spanners of weight O(1). wt(MST) can be constructed. We then consider spanners for complete graphs induced by a set of points in d-dimensional real normed space. The weight of an edge xy is the norm of the <(xy)over right arrow> vector. We show that for these graphs, t-spanners with total weight O(log n) wt(MST) can be constructed in polynomial time.
Let G = (V,E) be an n-vertex connected graph with positive edge weights. A subgraph G' = (V, E') is a t-spanner of G if for all u, v is an element of V, the weighted distance between u and v in G' is at mo...
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Let G = (V,E) be an n-vertex connected graph with positive edge weights. A subgraph G' = (V, E') is a t-spanner of G if for all u, v is an element of V, the weighted distance between u and v in G' is at most t times the weighted distance between u and v in G. We consider the problem of constructing sparse spanners. Sparseness of spanners is measured by two criteria, the size, defined as the number of edges in the spanner, and the weight, defined as the sum of the edge weights in the spanner. In this paper, we concentrate on constructing spanners of small weight. For an arbitrary positive edge-weighted graph G, for any t > 1, and any epsilon > 0, we show that a t-spanner of G with weight O(n(2+epsilon/t-1)). wt(MST) can be constructed in polynomial time. We also show that (log(2) n)-spanners of weight O(1). wt(MST) can be constructed. We then consider spanners for complete graphs induced by a set of points in d-dimensional real normed space. The weight of an edge xy is the norm of the <(xy)over right arrow> vector. We show that for these graphs, t-spanners with total weight O(log n) wt(MST) can be constructed in polynomial time.
We consider the expected performance of two greedy matching algorithms on sparse random graphs and also on random trees. In all cases we establish expressions for the mean and variance of the number of edges chosen an...
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We consider the expected performance of two greedy matching algorithms on sparse random graphs and also on random trees. In all cases we establish expressions for the mean and variance of the number of edges chosen and establish asymptotic normality.
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