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In this paper we show how to solve the Maximum Weight Stable Set Problem in a claw-free graph G ( V ,  E ) with α ( G ) ≤ 3 in time O ( | E | log | V | ) . More precisely, in time O ( | E | ) we check whether α ( G ) ≤ 3 or produce a stable set with cardinality at least 4; moreover, if α ( G ) ≤ 3 we produce in time O ( | E | log | V | ) a maximum weight stable set of G . This improves the bound of O ( | E | | V | ) due to Faenza, Oriolo and Stauffer.

(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image) In this paper we show how to solve the Maximum Weight Stable Set Problem in a claw-free graph G(V, E) with ... in time ... More precisely, in time ... we check whether ... or produce a stable set with cardinality at least 4; moreover, if ... we produce in time ... a maximum weight stable set of G. This improves the bound of ... due to Faenza, Oriolo and Stauffer.

The edge formulation of the stable set problem is defined by two-variable constraints, one for each edge of a graph G , expressing the simple condition that two adjacent nodes cannot belong to a stable set. We study the fractional stable set polytope , i.e. the polytope defined by the linear relaxation of the edge formulation. Even if this polytope is a weak approximation of the stable set polytope , its simple geometrical structure provides deep theoretical insight as well as interesting algorithmic opportunities. Exploiting a graphic characterization of the bases, we first redefine pivots in terms of simple graphic operations, that turn a given basis into an adjacent one. These results lead us to prove that the combinatorial diameter of the fractional stable set polytope is at most the number of nodes of the given graph. As a corollary, the Hirsch bound holds for this class of polytopes.

Given a directed graph G(V, A), the p-Median problem consists of determining p nodes (the median nodes) minimizing the total distance from the other nodes of the graph. We present a Branch-and-Cut-and-Price algorithm yielding provably good solutions for instances with |V|=3795. Key ingredients of the algorithm are a delayed column-and-row generation technique, exploiting the special structure of the formulation, to solve the LP-relaxation, and cutting planes to strengthen the formulation and limit the size of the enumeration tree. [PUBLICATION ABSTRACT]

We propose a pure 0-1 formulation for the wireless network design problem, i.e., the problem of configuring a set of transmitters to provide service coverage to a set of receivers. In contrast with classical mixed-integer formulations, where power emissions are represented by continuous variables, we consider only a finite set of power values. This has two major advantages: it better fits the usual practice and eliminates the sources of numerical problems that heavily affect continuous models. A crucial ingredient of our approach is an effective basic formulation for the single knapsack problem representing the coverage condition of a receiver. This formulation is based on the generalized upper bound (GUB) cover inequalities introduced by Wolsey [Wolsey L (1990) Valid inequalities for 0-1 knapsacks and mips with generalised upper bound constraints. Discrete Appl. Math. 29(2-3):251-261]; and its core is an extension of the exact formulation of the GUB knapsack polytope with two GUB constraints. This special case corresponds to the very common practical situation where only one major interferer is present. We assess the effectiveness of our formulation by comprehensive computational results over realistic instances of two typical technologies, namely, WiMAX and DVB-T. This paper was accepted by Dimitris Bertsimas, optimization.

Chronic venous leg ulceration can be managed by compression treatment, elevation of the leg, and exercise. The addition of ablative superficial venous surgery to this strategy has not been shown to affect ulcer healing, but does reduce ulcer recurrence. We aimed to assess healing and recurrence rates after treatment with compression with or without surgery in people with leg ulceration. We did venous duplex imaging of ulcerated or recently healed legs in 500 consecutive patients from three centres. We randomly allocated those with isolated superficial venous reflux and mixed superficial and deep reflux either compression treatment alone or in combination with superficial venous surgery. Compression consisted of multilayer compression bandaging every week until healing then class 2 below-knee stockings. Primary endpoints were 24-week healing rates and 12-month recurrence rates. Analysis was by intention to treat. 40 patients were lost to follow-up and were censored. Overall 24-week healing rates were similar in the compression and surgery and compression alone groups (65%vs 65%, hazard 0·84 [95% CI 0·77 to 1·24]; p=0·85) but 12-month ulcer recurrence rates were significantly reduced in the compression and surgery group (12%vs 28%, hazard −2·76 [95% CI −1·78 to −4·27]; p<0·0001). Adverse events were minimal and about equal in each group. Surgical correction of superficial venous reflux reduces 12-month ulcer recurrence. Most patients with chronic venous ulceration will benefit from the addition of simple venous surgery.

We propose a pure 0-1 formulation for the wireless network design problem, i.e., the problem of configuring a set of transmitters to provide service coverage to a set of receivers. In contrast with classical mixed-integer formulations, where power emissions are represented by continuous variables, we consider only a finite set of power values. This has two major advantages: it better fits the usual practice and eliminates the sources of numerical problems that heavily affect continuous models. A crucial ingredient of our approach is an effective basic formulation for the single knapsack problem representing the coverage condition of a receiver. This formulation is based on the generalized upper bound (GUB) cover inequalities introduced by Wolsey [Wolsey L (1990) Valid inequalities for 0-1 knapsacks and mips with generalised upper bound constraints. Discrete Appl. Math. 29(2-3):251-261]; and its core is an extension of the exact formulation of the GUB knapsack polytope with two GUB constraints. This special case corresponds to the very common practical situation where only one major interferer is present. We assess the effectiveness of our formulation by comprehensive computational results over realistic instances of two typical technologies, namely, WiMAX and DVB-T.

We propose a pure 0-1 formulation for the wireless network design problem, i.e., the problem of configuring a set of transmitters to provide service coverage to a set of receivers. In contrast with classical mixed-integer formulations, where power emissions are represented by continuous variables, we consider only a finite set of power values. This has two major advantages: it better fits the usual practice and eliminates the sources of numerical problems that heavily affect continuous models. A crucial ingredient of our approach is an effective basic formulation for the single knapsack problem representing the coverage condition of a receiver. This formulation is based on the generalized upper bound (GUB) cover inequalities introduced by Wolsey [Wolsey L (1990) Valid inequalities for 0-1 knapsacks and mips with generalised upper bound constraints. Discrete Appl. Math. 29(2-3):251-261]; and its core is an extension of the exact formulation of the GUB knapsack polytope with two GUB constraints. This special case corresponds to the very common practical situation where only one major interferer is present. We assess the effectiveness of our formulation by comprehensive computational results over realistic instances of two typical technologies, namely, WiMAX and DVB-T.

We propose a pure 0-1 formulation for the wireless network design problem, i.e., the problem of configuring a set of transmitters to provide service coverage to a set of receivers. In contrast with classical mixed-integer formulations, where power emissions are represented by continuous variables, we consider only a finite set of power values. This has two major advantages: it better fits the usual practice and eliminates the sources of numerical problems that heavily affect continuous models. A crucial ingredient of our approach is an effective basic formulation for the single knapsack problem representing the coverage condition of a receiver. This formulation is based on the generalized upper bound (GUB) cover inequalities introduced by Wolsey [Wolsey L (1990) Valid inequalities for 0-1 knapsacks and mips with generalised upper bound constraints. Discrete Appl. Math. 29(2-3):251-261]; and its core is an extension of the exact formulation of the GUB knapsack polytope with two GUB constraints. This special case corresponds to the very common practical situation where only one major interferer is present. We assess the effectiveness of our formulation by comprehensive computational results over realistic instances of two typical technologies, namely, WiMAX and DVB-T.