Declustering schemes allocate data blocks among multiple disks to enable parallel retrieval. Give... more Declustering schemes allocate data blocks among multiple disks to enable parallel retrieval. Given a declustering scheme D , its response time with respect to a query Q , rt ( Q ), is defined to be the maximum number of data blocks of the query stored by the scheme in any one of the disks. If | Q | is the number of data blocks in Q and M is the number of disks, then rt ( Q ) is at least ⌈| Q |/ M ⌉. One way to evaluate the performance of D with respect to a set of range queries Q is to measure its additive error ---the maximum difference of rt ( Q ) from ⌈| Q |/ M ⌉ over all range queries Q ∈ Q.In this article, we consider the problem of designing declustering schemes for uniform multidimensional data arranged in a d -dimensional grid so that their additive errors with respect to range queries are as small as possible. It has been shown that for a fixed dimension d ≥ 2, any declustering scheme on an M d grid, a grid with length M on each dimension, will always incur an additive erro...
A vertex k-labeling of graph G is distinguishing if the only automorphism that preserves the labe... more A vertex k-labeling of graph G is distinguishing if the only automorphism that preserves the labels of G is the identity map. The distinguishing number of G, D(G), is the smallest integer k for which G has a distinguishing k-labeling. In this paper, we apply the principle of inclusion-exclusion and develop recursive formulas to count the number of inequivalent distinguishing k-labelings of a graph. Along the way, we prove that the distinguishing number of a planar graph can be computed in time polynomial in the size of the graph. 1
In this paper, we consider the problem of counting and sampling structures in graphs. We define a... more In this paper, we consider the problem of counting and sampling structures in graphs. We define a class of "edge universal labeling problems"---which include proper $k$-colorings, independent sets, and downsets---and describe simple algorithms for counting and uniformly sampling valid labelings of graphs, assuming a path decomposition is given. Thus, we show that several well-studied counting and sampling problems are fixed parameter tractable (FPT) when parameterized by the pathwidth of the input graph. We discuss connections to counting and sampling problems for distributive lattices and, in particular, we give a new FPT algorithm for exactly counting and uniformly sampling stable matchings.
Proceedings of the 22nd ACM Conference on Economics and Computation, 2021
It is well known that every stable matching instance I has a rotation poset R(I) that can be comp... more It is well known that every stable matching instance I has a rotation poset R(I) that can be computed efficiently and the downsets of R(I) are in one-to-one correspondence with the stable matchings of I. Furthermore, for every poset P, an instance I(P) can be constructed efficiently so that the rotation poset of I(P) is isomorphic to P. In this case, we say that I(P) realizes P. Many researchers exploit the rotation poset of an instance to develop fast algorithms or to establish the hardness of stable matching problems. In order to gain a parameterized understanding of the complexity of sampling stable matchings, Bhatnagar et al.[1] introduced stable matching instances whose preference lists are restricted but nevertheless model situations that arise in practice. In this paper, we study four such parameterized restrictions. Our goal is to characterize the rotation posets that arise from these models: k-bounded, where each agent has at most k acceptable partners; k-attribute, where e...
Declustering schemes allocate data blocks among multiple disks to enable parallel retrieval. Give... more Declustering schemes allocate data blocks among multiple disks to enable parallel retrieval. Given a declustering scheme D , its response time with respect to a query Q , rt ( Q ), is defined to be the maximum number of data blocks of the query stored by the scheme in any one of the disks. If | Q | is the number of data blocks in Q and M is the number of disks, then rt ( Q ) is at least ⌈| Q |/ M ⌉. One way to evaluate the performance of D with respect to a set of range queries Q is to measure its additive error ---the maximum difference of rt ( Q ) from ⌈| Q |/ M ⌉ over all range queries Q ∈ Q.In this article, we consider the problem of designing declustering schemes for uniform multidimensional data arranged in a d -dimensional grid so that their additive errors with respect to range queries are as small as possible. It has been shown that for a fixed dimension d ≥ 2, any declustering scheme on an M d grid, a grid with length M on each dimension, will always incur an additive erro...
A vertex k-labeling of graph G is distinguishing if the only automorphism that preserves the labe... more A vertex k-labeling of graph G is distinguishing if the only automorphism that preserves the labels of G is the identity map. The distinguishing number of G, D(G), is the smallest integer k for which G has a distinguishing k-labeling. In this paper, we apply the principle of inclusion-exclusion and develop recursive formulas to count the number of inequivalent distinguishing k-labelings of a graph. Along the way, we prove that the distinguishing number of a planar graph can be computed in time polynomial in the size of the graph. 1
In this paper, we consider the problem of counting and sampling structures in graphs. We define a... more In this paper, we consider the problem of counting and sampling structures in graphs. We define a class of "edge universal labeling problems"---which include proper $k$-colorings, independent sets, and downsets---and describe simple algorithms for counting and uniformly sampling valid labelings of graphs, assuming a path decomposition is given. Thus, we show that several well-studied counting and sampling problems are fixed parameter tractable (FPT) when parameterized by the pathwidth of the input graph. We discuss connections to counting and sampling problems for distributive lattices and, in particular, we give a new FPT algorithm for exactly counting and uniformly sampling stable matchings.
Proceedings of the 22nd ACM Conference on Economics and Computation, 2021
It is well known that every stable matching instance I has a rotation poset R(I) that can be comp... more It is well known that every stable matching instance I has a rotation poset R(I) that can be computed efficiently and the downsets of R(I) are in one-to-one correspondence with the stable matchings of I. Furthermore, for every poset P, an instance I(P) can be constructed efficiently so that the rotation poset of I(P) is isomorphic to P. In this case, we say that I(P) realizes P. Many researchers exploit the rotation poset of an instance to develop fast algorithms or to establish the hardness of stable matching problems. In order to gain a parameterized understanding of the complexity of sampling stable matchings, Bhatnagar et al.[1] introduced stable matching instances whose preference lists are restricted but nevertheless model situations that arise in practice. In this paper, we study four such parameterized restrictions. Our goal is to characterize the rotation posets that arise from these models: k-bounded, where each agent has at most k acceptable partners; k-attribute, where e...
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Papers by Christine Cheng