28697628
Distributed Near-Optimal Matching
In this paper, we consider the following distributed bipartite matching problems: Let G=(L, R; E) be a bipartite graph in which boys are part L (left nodes), and girls are part R (right nodes.) There is an edge (li, rj) ∈ E iff boy li is interested in girl rj. Every boy li will propose to a girl rj among all those he is interested in, i.e., his adjacent right nodes in the bipartite graph G. If several boys propose to the same girl, only one of them will be accepted by the girl. We assume that none of the boys communicate with others. This matching problem is typical of distributed computing under incomplete information: Each boy only knows his own preference but none of the others. We first study the one-round matching problem: each boy proposes to at most one girl, so that the total number of girls receiving a proposal is maximized. If the maximum matching is M, then no deterministic algorithm can produce a matching of size not bounded by a constant, but a randomized algorithm achieves √M—and this is shown optimal by an adversary argument. If we allow many rounds in matching, with the senders learning from their failures, then the ratio is unbounded when the number of rounds is smaller than Δ, and becomes bounded (two) at the Δ-th round. In contrast, an extension of the one-round randomized algorithm establishes that there is no such discontinuity in the randomized case. This randomized result is also matched by an upper bound of asymptotically the same order.
4362564
More powerful closure operations on graphs
Abstract Bondy and Chvatal have observed the following result: G =( V , E ) is a simple graph of order n . If uv ∉ E and d ( u )+ d ( v )⩾ n , then G is Hamiltonian iff G + uv is Hamiltonian. Thus, we can obtain a graph C n ( G ), named the n -closure of G , from G by successively joining pairs of non-adjacent vertices whose degree sum is at least n . Therefore, G is Hamiltonian if C n ( G ) is Hamiltonian. Moreover, Bondy and Chvatal [2] generalized this idea to several properties on G . In the paper, we present some more powerful closure operations that extend the idea of Bondy and Chvatal.
30224685
Distributed near-optimal matching
AbstractIn this paper, we consider the following distributed bipartite matching problem: LetG=(L,R;E) be a bipartite graph in which boys are partL (left nodes), and girls are partR (right nodes.) There is an edge(li,rj)∈E iff boyli is interested in girlrj. Every boyli will propose to a girlrj among all those he is interested in, i.e., his adjacent right nodes in the bipartite graphG. If several boys propose to the same girl, only one of them will be accepted by the girl. We assume that none of the boys communicate with others. This matching problem is typical of distributed computing under incomplete information: Each boy only knows his own preference but none of the others. We first study the one-round matching problem: each boy proposes to at most one girl, so that the total number of girls receiving a proposal is maximized. If the maximum matching isM, then no deterministic algorithm can produce a matching of size not bounded by a constant, but a randomized algorithm achieves
$$\sqrt M -$$
 — and this is shown optimal by an adversary argument. If we allow many rounds in matching, with the senders learning from their failures, then, for deterministic algorithms, the ratio (of the optimal solution to the solution of the algorithm) is unbounded when the number of rounds is smaller than Δ(G), and becomes bounded (two) at the Δ(G)-th round. In contrast, an extension of the one-round randomized algorithm establishes that there is no such discontinuity in the randomized case. This randomized result is also matched by an upper bound of asymptotically the same order.
9765251
Minimum k Arborescences with
Bandwidth Constraints
Abstract
Let $G =(V,A)$ be a digraph with source $r$. A weight function
$w$ and bandwidth constraint function $b$ (positive integer) on
$A$ are given. We present algorithms for
finding $k$ $r$-arborescences in $G$
with minimum total weight and with bandwidth constraints.


11775174
Combined tag tracking and myocardium motion reconstruction from planar tagged MR image data without user-defined myocardial contours
We present a method for combined tag tracking and myocardium motion reconstruction from planar tagged MR image data that does not require user-defined myocardial contours. The method uses a cylindrical B-spline deformable model which more closely matches the shape of left ventricle than a Cartesian B-spline model. Experimental results on eight human imaging studies indicate that our method can track tag lines more accurately and faster than a previously proposed technique, which used manually determined myocardial contours. Also, circumferential strains computed by our method compare well with strains computed from expert edited tag lines using other deformation models.
41724019
A Resolution Based Framework to Explain Reasoning in Description Logics
As more complex applications are developed in Description Logics (DL), providing explanation services for DL reasoners becomes more crucial. We propose to use resolution proofs to construct explanations for unsatisfiability and inconsistency problems. Our approach is based on the observation that compared to natural deduction proofs, resolution technique is more focused, as all the literals involved in a proof contribute directly to the solution. Moreover, resolution can easily deal with global axioms (TBoxes) and assertions (ABoxes) which facilitates providing explanations w.r.t TBoxes and ABoxes. Our proposed explanation procedure1 is described as follows. First the explanation system communicates with a DL reasoner and retrieves the answer of a query. In the circumstances of unsatisfiability or inconsistency queries, the original DL axioms/assertions will be translated into first-order logic (FOL) formulas or clauses by the translation component. Then a resolution-based automated theorem prover is used to generate resolution proofs, taking the translated formulas or clauses as the input. The proofs are then sent back to the explanation module to be transformed for better human understanding. Since the order of selecting clauses during the resolution procedure has significant effect on the quality of explanations and it is difficult to be fully controlled, our approach uses a refutation graph as a guide for this transformation. A refutation graph is a graph whose nodes are literals (grouped together in clauses) and its edges connect contradictory literals. In such a graph, contradictory literals between input clauses are directly visible, which can be used as heuristics to guide the explanation process. The main idea of explanation based on the refutation graph is to start from a literal node (or nodes) and traverse the graph. The traversal order is decided by a preference assigned to each node. For example, the axiom A v B is more appropriate to be considered as an inference rule to explain B is the consequence of A than considering ¬A is the consequence of ¬B, and hence accordingly there is a preference to start from A instead of B. Finally, the resolution proof is traced back to the contributing FOL formulas and later transformed into natural language explanations. We are planning to extend our work to explain subsumption, satisfiability, and non subsumption queries. An implementation of the proposed framework is underway.
30339202
On Computing and Drawing Maxmin-Height Covering Triangulation
Given a simple polygon P, a covering triangulation is another triangulation over the vertices of P and some inner Steiner points (see Fig 1 for a covering triangulation generated by our heuristic). In other words, when computing a covering triangulation one is only allowed to add Steiner points in the interior of P. This problem is originally from mesh smoothing: one is not happy with the mesh over a specific region (say P) and would like to re-triangulate that region. Certainly, adding Steiner points on the boundary of P would destroy the neighboring part of P and would result in further changes of the mesh.