Convex Combinatorial Optimization

Convex Combinatorial Optimization (2004)

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by Shmuel Onn , Uriel G. Rothblum

Venue:	DISCRETE & COMPUTATIONAL GEOMETRY
Citations:	12 - 6 self

BibTeX

@MISC{Onn04convexcombinatorial,
    author = {Shmuel Onn and Uriel G. Rothblum},
    title = { Convex Combinatorial Optimization },
    year = {2004}
}

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Abstract

We introduce the convex combinatorial optimization problem, a far-reaching generalization of the standard linear combinatorial optimization problem. We show that it is strongly polynomial time solvable over any edge-guaranteed family, and discuss several applications.

Citations

969	Geometric algorithms and combinatorial optimization - Grötschel, Lovász, et al. - 1993
306	A polynomial algorithm in linear programming, Doklady Akad - Khachiyan - 1979
281	Theoretical improvements in algorithmic efficiency for network flow problems - Edmonds, Karp - 1970
253	Maximum matching and a polyhedron with (0,1)-vertices - Edmonds - 1965
228	Convex Polytopes - Grunbaum - 1967
188	Combinatorial Optimization - Cook, Cunningham, et al. - 1998
146	K: A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra. Discrete Comput Geom - Avis, Fukuda - 1992
138	How good is the simplex algorithm - Klee, Minty - 1969
116	facing up to arrangements: face-count formulas for partitions of space by hyperplanes - Zaslavsky - 1975
101	Constructing arrangements of lines and hyperplanes with applications - Edelsbrunner, O’Rourke, et al. - 1986
84	Network Flows and Monotropic Optimization - Rockafellar - 1984
82	Matroids and the greedy algorithm - EDMONDS - 1971
79	H.: The quadratic assignment problem: A survey and recent developments - Pardalos, Rendl, et al. - 1994
67	Fiber polytopes - Billera
42	The d-step conjecture and its relatives - Klee, Kleinschmidt - 1987
31	On the zone theorem for hyperplane arrangements - Edelsbrunner, Seidel, et al. - 1993
28	Improved algorithms for bipartite network flow - Ahuja, Orlin, et al. - 1994
25	A polynomial time algorithm for shaped partition problems - Hwang, Onn, et al. - 1999
22	P.L.: On clustering problems with connected optima in Euclidean spaces - Boros, Hammer - 1989
20	U.G.: Optimal partitions having disjoint convex and conic hulls - Barnes, Hoffman, et al. - 1992
20	Partition of Space - Buck - 1943
19	L.J.: The vector partition problem for convex objective functions - Onn, Schulman
18	programming, the simplex algorithm and simple polytopes - Kalai, Linear - 1997
18	G.M.: (0, 1)-integer programming: optimization and augmentation are equivalent - Schulz, Weismantel, et al. - 1995
17	E.: An application of simultaneous Diophantine approximation in combinatorial optimization - Frank, Tardos - 1987
16	Separable partitions - Alon, Onn - 1999
14	Ancient and new algorithms for load balancing in the Lp norm - Avidor, Azar, et al. - 1998
13	Consecutive optimizers for a partitioning problem with applications to optimal inventory groupings for joint replenishment - Chakravarty, Orlin, et al. - 1985
12	The number of partitions of a set of n points in k dimensions induced by hyperplanes - Harding - 1967
10	complexity and combinatorics of permutation polytopes, Journal of Combinatorial Theory Series A 64:31–49 - Onn, Geometry - 1993
9	Variations of cost functions - Sturmfels, Thomas
8	All 0-1 polytopes are traveling salesman polytopes - Billera, Sarangarajan - 1996
8	The Pareto set of the partition bargaining game - Granot, Rothblum - 1991
7	B.: Minkowski addition of polytopes: complexity and applications to Gröbner bases - Gritzmann, Sturmfels - 1993
7	asymmetric Schur-convexity and optimality of consecutive partitions - Hwang, Rothblum, et al. - 1996
7	Onn S.: On the diameter of convex polytopes - Kleinschmidt - 1992
7	Convex matroid optimization - Onn
6	E.: A polynomial case of unconstrained zero-one quadratic optimization - Allemand, Fukuda, et al.
6	R.: The complexity of generic primal algorithms for solving general integral programs - Schulz, Weismantel
5	V.: An adaptive algorithm for vector partitioning - Fukuda, Onn, et al.
5	A.: Maximizing classes of two-parameter objectives over matroids - Hassin, Tamir - 1989
4	L.: Combinatorial optimization. In: Handbook of Combinatorics - Grötschel, Lovász - 1995
3	Momentopes and the vertex complexity of partition polytopes - Aviran, Onn
3	Lattice-free polytopes and their diameter - Deza, Onn - 1995
3	Maximizing the product of two linear functions - Hammer, Hansen, et al. - 1997
2	The Hirsch conjecture is true for (0 - Naddef
1	Edge-directions of polyhedra with applications to network flows, forthcoming - Onn, Rothblum, et al.