31 research outputs found
All solution graphs in multidimensional screening
We study general discrete-types multidimensional screening without any noticeable restrictions on valuations, using instead epsilon-relaxation of the incentive-compatibility constraints. Any active (becoming equality) constraint can be perceived as "envy" arc from one type to another, so the set of active constraints is a digraph. We find that: (1) any solution has an in-rooted acyclic graph ("river"); (2) for any logically feasible river there exists a screening problem resulting in such river. Using these results, any solution is characterized both through its spanning-tree and through its Lagrange multipliers, that can help in finding solutions and their efficiency/distortion properties.incentive compatibility; multidimensional screening; second-degree price discrimination; non-linear pricing; graphs
All solution graphs in multidimensional screening
We study general discrete-types multidimensional screening without any
noticeable restrictions on valuations, using instead epsilon-relaxation of the incentive-compatibility constraints. Any active (becoming
equality) constraint can be perceived as "envy" arc from one type to another, so the set of active
constraints is a digraph. We find that: (1) any solution has an in-rooted
acyclic graph ("river"); (2) for any
logically feasible river there exists a screening problem resulting in such
river. Using these results, any solution is characterized both through its
spanning-tree and through its Lagrange multipliers, that can help in finding
solutions and their efficiency/distortion properties
All solution graphs in multidimensional screening
We study general discrete-types multidimensional screening without any
noticeable restrictions on valuations, using instead epsilon-relaxation of the incentive-compatibility constraints. Any active (becoming
equality) constraint can be perceived as "envy" arc from one type to another, so the set of active
constraints is a digraph. We find that: (1) any solution has an in-rooted
acyclic graph ("river"); (2) for any
logically feasible river there exists a screening problem resulting in such
river. Using these results, any solution is characterized both through its
spanning-tree and through its Lagrange multipliers, that can help in finding
solutions and their efficiency/distortion properties
The Edmonds-Giles Conjecture and its Relaxations
Given a directed graph, a directed cut is a cut with all arcs oriented in the same direction, and a directed join is a set of arcs which intersects every directed cut at least once. Edmonds and Giles conjectured for all weighted directed graphs, the minimum weight of a directed cut is equal to the maximum size of a packing of directed joins. Unfortunately, the conjecture is false; a counterexample was first given by Schrijver. However its âdualâ statement, that the minimum weight of a dijoin is equal to the maximum number of dicuts in a packing, was shown to be true by Luchessi and Younger.
Various relaxations of the conjecture have been considered; Woodallâs conjecture remains open, which asks the same question for unweighted directed graphs, and Edmond- Giles conjecture was shown to be true in the special case of source-sink connected directed graphs. Following these inquries, this thesis explores different relaxations of the Edmond- Giles conjecture
On Box-Perfect Graphs
Let be a graph and let be the clique-vertex incidence matrix
of . It is well known that is perfect iff the system , is totally dual integral (TDI). In 1982,
Cameron and Edmonds proposed to call box-perfect if the system
, is box-totally dual
integral (box-TDI), and posed the problem of characterizing such graphs. In
this paper we prove the Cameron-Edmonds conjecture on box-perfectness of parity
graphs, and identify several other classes of box-perfect graphs. We also
develop a general and powerful method for establishing box-perfectness
On the characterization of the domination of a diameter-constrained network reliability model
AbstractLet G=(V,E) be a digraph with a distinguished set of terminal vertices KâV and a vertex sâK. We define the s,K-diameter of G as the maximum distance between s and any of the vertices of K. If the arcs fail randomly and independently with known probabilities (vertices are always operational), the diameter-constrained s,K-terminal reliability of G, Rs,K(G,D), is defined as the probability that surviving arcs span a subgraph whose s,K-diameter does not exceed D.The diameter-constrained network reliability is a special case of coherent system models, where the domination invariant has played an important role, both theoretically and for developing algorithms for reliability computation. In this work, we completely characterize the domination of diameter-constrained network models, giving a simple rule for computing its value: if the digraph either has an irrelevant arc, includes a directed cycle or includes a dipath from s to a node in K longer than D, its domination is 0; otherwise, its domination is -1 to the power |E|-|V|+1. In particular this characterization yields the classical source-to-K-terminal reliability domination obtained by Satyanarayana.Based on these theoretical results, we present an algorithm for computing the reliability