59,817 research outputs found
SAT Modulo Monotonic Theories
We define the concept of a monotonic theory and show how to build efficient
SMT (SAT Modulo Theory) solvers, including effective theory propagation and
clause learning, for such theories. We present examples showing that monotonic
theories arise from many common problems, e.g., graph properties such as
reachability, shortest paths, connected components, minimum spanning tree, and
max-flow/min-cut, and then demonstrate our framework by building SMT solvers
for each of these theories. We apply these solvers to procedural content
generation problems, demonstrating major speed-ups over state-of-the-art
approaches based on SAT or Answer Set Programming, and easily solving several
instances that were previously impractical to solve
Low-Degree Spanning Trees of Small Weight
The degree-d spanning tree problem asks for a minimum-weight spanning tree in
which the degree of each vertex is at most d. When d=2 the problem is TSP, and
in this case, the well-known Christofides algorithm provides a
1.5-approximation algorithm (assuming the edge weights satisfy the triangle
inequality).
In 1984, Christos Papadimitriou and Umesh Vazirani posed the challenge of
finding an algorithm with performance guarantee less than 2 for Euclidean
graphs (points in R^n) and d > 2. This paper gives the first answer to that
challenge, presenting an algorithm to compute a degree-3 spanning tree of cost
at most 5/3 times the MST. For points in the plane, the ratio improves to 3/2
and the algorithm can also find a degree-4 spanning tree of cost at most 5/4
times the MST.Comment: conference version in Symposium on Theory of Computing (1994
Smoothed Analysis of the Minimum-Mean Cycle Canceling Algorithm and the Network Simplex Algorithm
The minimum-cost flow (MCF) problem is a fundamental optimization problem
with many applications and seems to be well understood. Over the last half
century many algorithms have been developed to solve the MCF problem and these
algorithms have varying worst-case bounds on their running time. However, these
worst-case bounds are not always a good indication of the algorithms'
performance in practice. The Network Simplex (NS) algorithm needs an
exponential number of iterations for some instances, but it is considered the
best algorithm in practice and performs best in experimental studies. On the
other hand, the Minimum-Mean Cycle Canceling (MMCC) algorithm is strongly
polynomial, but performs badly in experimental studies.
To explain these differences in performance in practice we apply the
framework of smoothed analysis. We show an upper bound of
for the number of iterations of the MMCC algorithm.
Here is the number of nodes, is the number of edges, and is a
parameter limiting the degree to which the edge costs are perturbed. We also
show a lower bound of for the number of iterations of the
MMCC algorithm, which can be strengthened to when
. For the number of iterations of the NS algorithm we show a
smoothed lower bound of .Comment: Extended abstract to appear in the proceedings of COCOON 201
Enhancing Domain Word Embedding via Latent Semantic Imputation
We present a novel method named Latent Semantic Imputation (LSI) to transfer
external knowledge into semantic space for enhancing word embedding. The method
integrates graph theory to extract the latent manifold structure of the
entities in the affinity space and leverages non-negative least squares with
standard simplex constraints and power iteration method to derive spectral
embeddings. It provides an effective and efficient approach to combining entity
representations defined in different Euclidean spaces. Specifically, our
approach generates and imputes reliable embedding vectors for low-frequency
words in the semantic space and benefits downstream language tasks that depend
on word embedding. We conduct comprehensive experiments on a carefully designed
classification problem and language modeling and demonstrate the superiority of
the enhanced embedding via LSI over several well-known benchmark embeddings. We
also confirm the consistency of the results under different parameter settings
of our method.Comment: ACM SIGKDD 201
I/O-optimal algorithms on grid graphs
Given a graph of which the n vertices form a regular two-dimensional grid,
and in which each (possibly weighted and/or directed) edge connects a vertex to
one of its eight neighbours, the following can be done in O(scan(n)) I/Os,
provided M = Omega(B^2): computation of shortest paths with non-negative edge
weights from a single source, breadth-first traversal, computation of a minimum
spanning tree, topological sorting, time-forward processing (if the input is a
plane graph), and an Euler tour (if the input graph is a tree). The
minimum-spanning tree algorithm is cache-oblivious. The best previously
published algorithms for these problems need Theta(sort(n)) I/Os. Estimates of
the actual I/O volume show that the new algorithms may often be very efficient
in practice.Comment: 12 pages' extended abstract plus 12 pages' appendix with details,
proofs and calculations. Has not been published in and is currently not under
review of any conference or journa
Improving the Asymmetric TSP by Considering Graph Structure
Recent works on cost based relaxations have improved Constraint Programming
(CP) models for the Traveling Salesman Problem (TSP). We provide a short survey
over solving asymmetric TSP with CP. Then, we suggest new implied propagators
based on general graph properties. We experimentally show that such implied
propagators bring robustness to pathological instances and highlight the fact
that graph structure can significantly improve search heuristics behavior.
Finally, we show that our approach outperforms current state of the art
results.Comment: Technical repor
- …