Results 1  10
of
86
Shock Graphs and Shape Matching
, 1997
"... We have been developing a theory for the generic representation of 2D shape, where structural descriptions are derived from the shocks (singularities) of a curve evolution process, acting on bounding contours. We now apply the theory to the problem of shape matching. The shocks are organized into a ..."
Abstract

Cited by 270 (37 self)
 Add to MetaCart
(Show Context)
We have been developing a theory for the generic representation of 2D shape, where structural descriptions are derived from the shocks (singularities) of a curve evolution process, acting on bounding contours. We now apply the theory to the problem of shape matching. The shocks are organized into a directed, acyclic shock graph, and complexity is managed by attending to the most significant (central) shape components first. The space of all such graphs is highly structured and can be characterized by the rules of a shock graph grammar. The grammar permits a reduction of a shock graph to a unique rooted shock tree. We introduce a novel tree matching algorithm which finds the best set of corresponding nodes between two shock trees in polynomial time. Using a diverse database of shapes, we demonstrate our system's performance under articulation, occlusion, and changes in viewpoint.
ViewBased Object Recognition Using Saliency Maps
, 1998
"... We introduce a novel viewbased object representation, called the saliency map graph (SMG), which captures the salient regions of an object view at multiple scales using a wavelet transform. This compact representation is highly invariant to translation, rotation (image and depth), and scaling, and ..."
Abstract

Cited by 54 (10 self)
 Add to MetaCart
We introduce a novel viewbased object representation, called the saliency map graph (SMG), which captures the salient regions of an object view at multiple scales using a wavelet transform. This compact representation is highly invariant to translation, rotation (image and depth), and scaling, and offers the locality of representation required for occluded object recognition. To compare two saliency map graphs, we introduce two graph similarity algorithms. The first computes the topological similarity between two SMG's, providing a coarselevel matching of two graphs. The second computes the geometrical similarity between two SMG's, providing a finelevel matching of two graphs. We test and compare these two algorithms on a large database of model object views.
Satisfiability Solvers
, 2008
"... The past few years have seen an enormous progress in the performance of Boolean satisfiability (SAT) solvers. Despite the worstcase exponential run time of all known algorithms, satisfiability solvers are increasingly leaving their mark as a generalpurpose tool in areas as diverse as software and h ..."
Abstract

Cited by 48 (0 self)
 Add to MetaCart
The past few years have seen an enormous progress in the performance of Boolean satisfiability (SAT) solvers. Despite the worstcase exponential run time of all known algorithms, satisfiability solvers are increasingly leaving their mark as a generalpurpose tool in areas as diverse as software and hardware verification [29–31, 228], automatic test pattern generation [138, 221], planning [129, 197], scheduling [103], and even challenging problems from algebra [238]. Annual SAT competitions have led to the development of dozens of clever implementations of such solvers [e.g. 13,
Engineering an Efficient Canonical Labeling Tool for Large and Sparse Graphs
"... The problem of canonically labeling a graph is studied. Within the general framework of backtracking algorithms based on individualization and refinement, data structures, subroutines, and pruning heuristics especially for fast handling of large and sparse graphs are developed. Experiments indicate ..."
Abstract

Cited by 44 (1 self)
 Add to MetaCart
The problem of canonically labeling a graph is studied. Within the general framework of backtracking algorithms based on individualization and refinement, data structures, subroutines, and pruning heuristics especially for fast handling of large and sparse graphs are developed. Experiments indicate that the algorithm implementation in most cases clearly outperforms existing stateoftheart tools.
Determining Acceptance Possibility for a Quantum Computation is Hard for PH
, 1997
"... It is shown that determining whether a quantum computation has a nonzero probability of accepting is at least as hard as the polynomial time hierarchy. This hardness ..."
Abstract

Cited by 34 (4 self)
 Add to MetaCart
It is shown that determining whether a quantum computation has a nonzero probability of accepting is at least as hard as the polynomial time hierarchy. This hardness
Containment of Conjunctive Queries on Annotated Relations
"... We study containment and equivalence of (unions of) conjunctive queries on relations annotated with elements of a commutative semiring. Such relations and the semantics of positive relational queries on them were introduced in a recent paper as a generalization of set semantics, bag semantics, incom ..."
Abstract

Cited by 30 (6 self)
 Add to MetaCart
(Show Context)
We study containment and equivalence of (unions of) conjunctive queries on relations annotated with elements of a commutative semiring. Such relations and the semantics of positive relational queries on them were introduced in a recent paper as a generalization of set semantics, bag semantics, incomplete databases, and databases annotated with various kinds of provenance information. We obtain positive decidability results and complexity characterizations for databases with lineage, whyprovenance, and provenance polynomial annotations, for both conjunctive queries and unions of conjunctive queries. At least one of these results is surprising given that provenance polynomial annotations seem “more expressive ” than bag semantics and under the latter, containment of unions of conjunctive queries is known to be undecidable. The decision procedures rely on interesting variations on the notion of containment mappings. We also show that for any positive semiring (a very large class) and conjunctive queries without selfjoins, equivalence is the same as isomorphism. 1.
Completeness results for Graph Isomorphism
, 2002
"... We prove that the graph isomorphism problem restricted to trees and to colored graphs with color multiplicities 2 and 3 is manyone complete for several complexity classes within NC². In particular we show that tree isomorphism, when trees are encoded as strings, is NC¹hard under AC0reductions ..."
Abstract

Cited by 28 (9 self)
 Add to MetaCart
We prove that the graph isomorphism problem restricted to trees and to colored graphs with color multiplicities 2 and 3 is manyone complete for several complexity classes within NC². In particular we show that tree isomorphism, when trees are encoded as strings, is NC¹hard under AC0reductions. NC¹completeness thus follows from Buss's NC¹ upper bound. By contrast, we prove that testing isomorphism of two trees encoded as pointer lists is Lcomplete. Concerning colored graphs we show that the isomorphism problem for graphs with color multiplicities 2 and 3 is complete for symmetric logarithmic space SL under manyone reductions. This result improves the existing upper bounds for the problem. We also show that the graph automorphism problem for colored graphs with color classes of size 2 is equivalent to deciding whether a graph has more than a single connected component and we prove that for color classes of size 3 the graph automorphism problem is contained in SL.
Quantum algorithms for algebraic problems
, 2008
"... Quantum computers can execute algorithms that dramatically outperform classical computation. As the bestknown example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for classical computers. Understanding what other computational pro ..."
Abstract

Cited by 23 (1 self)
 Add to MetaCart
Quantum computers can execute algorithms that dramatically outperform classical computation. As the bestknown example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for classical computers. Understanding what other computational problems can be solved significantly faster using quantum algorithms is one of the major challenges in the theory of quantum
The Boolean Isomorphism Problem
 SIAM JOURNAL ON COMPUTING
, 1996
"... We investigate the computational complexity of the Boolean Isomorphism problem (BI): on input of two Boolean formulas F and G decide whether there exists a permutation of the variables of G such that F and G become equivalent. Our main result is a oneround interactive proof for BI, where the verifi ..."
Abstract

Cited by 22 (2 self)
 Add to MetaCart
(Show Context)
We investigate the computational complexity of the Boolean Isomorphism problem (BI): on input of two Boolean formulas F and G decide whether there exists a permutation of the variables of G such that F and G become equivalent. Our main result is a oneround interactive proof for BI, where the verifier has access to an NP oracle. To obtain this, we use a recent result from learning theory by Bshouty et.al. that Boolean formulas can be learned probabilistically with equivalence queries and access to an NP oracle. As a consequence, BI cannot be \Sigma p 2 complete unless the Polynomial Hierarchy collapses. This solves an open problem posed in [BRS95]. Further properties of BI are shown: BI has And and Orfunctions, the counting version, #BI, can be computed in polynomial time relative to BI, and BI is selfreducible.
THE HIDDEN SUBGROUP PROBLEM  REVIEW AND OPEN PROBLEMS
, 2004
"... An overview of quantum computing and in particular the Hidden Subgroup Problem are presented from a mathematical viewpoint. Detailed proofs are supplied for many important results from the literature, and notation is unified, making it easier to absorb the background necessary to begin research on ..."
Abstract

Cited by 19 (1 self)
 Add to MetaCart
An overview of quantum computing and in particular the Hidden Subgroup Problem are presented from a mathematical viewpoint. Detailed proofs are supplied for many important results from the literature, and notation is unified, making it easier to absorb the background necessary to begin research on the Hidden Subgroup Problem. Proofs are provided which give very concrete algorithms and bounds for the finite abelian case with little outside references, and future directions are provided for the nonabelian case. This summary is current as of October 2004.