G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. Marchetti-Spaccamela, and M. Protasi. Complexity and Approximation. Combinatorial Optimization Problems and their Approximability Properties. Springer, Berlin, 1999.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the inference rule that leaves the fewest number of unresolved genotypes in the end. This problem was studied by Gus eld, who proved it is NP hard and APX hard in [40] A problem is APX hard if there is a constant 1 such that the existence of an approximation algorithm would imply P=NP. See [3] for a full description of the class APX) As for practical algorithms, Gus eld [41] proposed an integer programming approach for a graph theoretic formulation of the problem. The problem is rst transformed (by an exponential time reduction) into a problem on a digraph G = N; A) de ned as ....

G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. MarchettiSpaccamela, and M. Protasi. Complexity and Approximation. Combinatorial Optimization Problems and their Approximability Properties. Springer, Berlin, 1999.

....finally WJISP with arbitrary lengths. We consider a class of simple deterministic algorithms for WJISP and investigate so called worst case ratios (or approximation ratios) that can be obtained by algorithms within this class. Using standard terminology (see e.g. Hochbaum [17] Ausiello et al. [1]) we say that a deterministic algorithm for WJISP achieves (approximation) ratio # if it always outputs a feasible solution whose weight is at least as large as 1 # times the weight of an optimal solution. A randomized algorithm achieves approximation ratio # if, on every instance of WJISP, the ....

....in the original instance (only intervals with integral starting times must be considered) 3 Algorithm GREEDY# We propose a myopic algorithm called GREEDY # , shown in Figure 1, as an approximation algorithm for WJISP. It has a parameter # that can take (meaningful) values in the range [0, 1]. GREEDY # considers the intervals in order of non decreasing right endpoint. It maintains a set S of currently selected intervals. When it processes an interval i, it computes a set C i S such that i could be selected after preempting the intervals in C i and such that C i has minimum weight ....

G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. Marchetti-Spaccamela, and M. Protasi. Complexity and Approximation. Combinatorial Optimization Problems and their Approximability Properties. Springer, Berlin, 1999.

....: v C ; this is a potentially much smaller Kneser representation. The problem of finding a Kneser representation with the smallest ground set, i.e. the smallest C, is the minimum clique cover for the complement of G, and hence NP complete and hard to approximate; see, e.g. Ausiello et al. [2]. Simplicial complexes. We use letters like K, L, to denote simplicial complexes. See, e.g. 16] 4] 14] for more background) We consider only finite simplicial complexes, so a simplicial complex K is a nonempty hereditary set system (i.e. S K and S # S implies S # K) in ....

.... complex, then #K is the first barycentric subdivision of K, also denoted by sd K (the empty simplex is not a vertex of the barycentric subdivision, and this is the reason for removing in the definition of #F ) The (twofold) deleted join of K, denoted by K #2 # , has vertex set V (K)[2] (two copies of V (K) and the simplices are S S 2 : S 1 , S 2 K, S 1 S 2 = # , where we use the shorthand S 1 S 2 : S 1 1 ) # (S 2 2 ) Z 2 spaces and Z 2 index. A Z 2 space (also called antipodality space in the literature) is a pair (T , #) where T is a topological ....

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G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. Marchetti-Spaccamela, and M. Protasi, Complexity and Approximation. Combinatorial optimization problems and their approximability properties, Springer-Verlag, 1999.

....be approximated within a factor of (k 1) 2 if all paths 2 PRELIMINARIES 3 have length at most k. Then we give approximation algorithms achieving a better approximation ratio for k = 2; 3; 4. We also prove that MaxToR is APX complete for paths of bounded length. APX completeness (see e.g. [2]) implies that MaxToR cannot be approximated within a certain constant factor unless P = NP, even for instances with short paths. Finally, we have implemented our approximation algorithm and obtained very encouraging results on real data sets. Independently of our work, Di Battista, Patrignani ....

....ratios for instances containing only paths of length at most k for k = 2; 3; 4. Finally, we prove APX completeness for instances where the path length is bounded by an arbitrary constant, by an approximation preserving reduction from the Max2SAT problem, which is well known to be APX complete [2]. 5.1 A simple constant factor approximation algorithm For paths of constant length there is a very easy randomized approximation algorithm: just select the directions of the edges independently at random. If each edge is oriented in one of the two possible ways with probability 1 2, a path of ....

G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. Marchetti-Spaccamela, and M. Protasi. Complexity and Approximation. Combinatorial Optimization Problems and their Approximability Properties. Springer, Berlin, 1999.

....Independent Set, i.e. if Cut Packing can be O(f(n) approximated in polynomial time, so can Independent Set. Plugging in the most recent inapproximability results for Independent Set (see [13] yields the following corollary (for a de nition of ZPP the interested reader can consult, for example, [3]) Corollary 2.3 The existence of a O(n 1 ) approximation algorithm for Cut Packing, for any 0, implies NP ZPP. The existence of a O(n 1=2 ) approximation algorithm for Cut Packing, for any xed 0, implies P = NP. We now turn to a new result, showing that, for the same graph G, ....

G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. Marchetti-Spaccamela, M. Protasi, Combinatorial Optimization Problems and their Approximability Properties, SpringerVerlag, Berlin (1999).

....: x n g, with the additional restriction that each variable appears in at most 3 of the clauses, counting together both positive and negative occurrences. The optimization problem calls for a truth assignment that satis es as many clauses as possible. It is known that Max 2 Sat 3 is APX hard [1, 4]. Theorem 1 Cycle Packing is APX hard, even for graphs with maximum degree 3. Proof: Given an input to Max 2 Sat 3, let X = fx 1 ; x n g denote the set of variables and C = fc 1 ; c m g the set of clauses. Furthermore, denote by m i the number of occurrences of x i . We will ....

G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. Marchetti-Spaccamela, M. Protasi, Combinatorial Optimization Problems and their Approximability Properties, SpringerVerlag, Berlin (1999).

.... graph theoretic optimisation problems remain NP hard when the input is restricted to graphs of bounded or regular degree, even when the maximum degree of the graph is 3, e.g. Maximum Independent Set [10, problem GT20] and Minimum Dominating Set [10, problem GT2] to name but two (see, for example, [1] for recent results on the complexity and approximability of these problems) In this paper we introduce a technique that may be used to analyse the worst case performance of greedy algorithms on cubic graphs. The technique uses linear programming and may be applied to a variety of graph theoretic ....

G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. Marchetti-Spaccamela and M. Protasi. Complexity and Approximation. Combinatorial Optimization Problems and their Approximability Properties. Springer-Verlag, 1999.

....fact online. For NPhard problems, polynomial time approximation algorithms offer a way to trade solution quality for computation time. Polynomial time approximation algorithms have intensively been considered within the last years. Comprehensive surveys on approximation algorithms can be found in [38, 31, 7, 48]. Example 3.7 (Load Balancing on Identical Machines revisited) Consider the load balancing problem described in Exampe 3.3. Graham [27, 28] proposed the following greedytype heuristic LIST: Consider the jobs in order of their occurence in the input sequence I. Always assign the next job to the ....

G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. Marchetti-Spaccamela, and M. Protasi, Complexity and approximation. combinatorial optimization problems and their approximability properties, Springer, 1999.

....a pair of nodes. The value of a cut (A; B) is the ratio of the total capacity and the total demand between the sets A and B. So it is the ratio of the number edges in E crossing the cut and the number of edges in F crossing the cut. Deciding the minimum such ratio cut is an NP hard problem (cf. [2]) First we show how to transform an instance of this problem so that the sets E and F are disjoint, without modi ng the value of the minimum cut. For every edge (a; b) 2 E F we create a new node ab, and exchange the edge in E with the edges (a; ab) and (b; ab) For a cut with a and b in the ....

G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. Marchetti Spaccamela and M. Protasi. Complexity and Approximation. Combinatorial Optimization Problems and their Approximability Properties, to appear, Springer-Verlag, Berlin.

....a pair of nodes. The value of a cut (A; B) is the ratio of the total capacity and the total demand between the sets A and B. So it is the ratio of the number edges in E crossing the cut and the number of edges in F crossing the cut. Deciding the minimum such ratio cut is an NP hard problem (cf. [2]) First we show how to transform an instance of this problem so that the sets E and F are disjoint, without modifing the value of the minimum cut. For every edge (a; b) 2 E F we create a new node ab, and exchange the edge in E with the edges (a; ab) and (b; ab) For a cut with a and b in the ....

G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. Marchetti Spaccamela and M. Protasi. Complexity and Approximation. Combinatorial Optimization Problems and their Approximability Properties, to appear, Springer-Verlag, Berlin.

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G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. Marchetti-Spaccamela, and M. Protasi. Complexity and Approximation. Combinatorial Optimization Problems and their Approximability Properties. Springer, Berlin, 1999.

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G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. Marchetti-Spaccamela, M. Protasi, Combinatorial Optimization Problems and their Approximability Properties, SpringerVerlag, Berlin (1999).

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G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. Marchetti-Spaccamela, and M. Protasi, Complexity and Approximation. Combinatorial optimization problems and their approximability properties, Springer-Verlag, 1999.

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G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. Marchetti-Spaccamela, and M. Protasi. Complexity and Approximation. Combinatorial Optimization Problems and their Approximability Properties. Springer-Verlag, Berlin, 1999.

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G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. Marchetti-Spaccamela, and M. Protasi. Complexity and Approximation. Combinatorial optimization problems and their approximability properties. Springer-Verlag, 1999.

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G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. Marchetti-Spaccamela, and M. Protasi. Complexity and Approximation. Combinatorial Optimization Problems and their Approximability Properties. Springer, Berlin, 1999.

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G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. Marchetti Spaccamela and M. Protasi. Complexity and Approximation. Combinatorial Optimization Problems and their Approximability Properties, to appear, Springer-Verlag, Berlin.

No context found.

G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. Marchetti-Spaccamela, and M. Protasi, Complexity and Approximation. Combinatorial Optimization Problems and Their Approximability Properties. Springer-Verlag, Berlin, 1999.

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G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. Marchetti-Spaccamela, and M. Protasi. Complexity and Approximation. Combinatorial Optimization Problems and their Approximability Properties. Springer, Berlin, 1999.

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