2,737 research outputs found
A Satisfiability Algorithm for Sparse Depth Two Threshold Circuits
We give a nontrivial algorithm for the satisfiability problem for cn-wire
threshold circuits of depth two which is better than exhaustive search by a
factor 2^{sn} where s= 1/c^{O(c^2)}. We believe that this is the first
nontrivial satisfiability algorithm for cn-wire threshold circuits of depth
two. The independently interesting problem of the feasibility of sparse 0-1
integer linear programs is a special case. To our knowledge, our algorithm is
the first to achieve constant savings even for the special case of Integer
Linear Programming. The key idea is to reduce the satisfiability problem to the
Vector Domination Problem, the problem of checking whether there are two
vectors in a given collection of vectors such that one dominates the other
component-wise.
We also provide a satisfiability algorithm with constant savings for depth
two circuits with symmetric gates where the total weighted fan-in is at most
cn.
One of our motivations is proving strong lower bounds for TC^0 circuits,
exploiting the connection (established by Williams) between satisfiability
algorithms and lower bounds. Our second motivation is to explore the connection
between the expressive power of the circuits and the complexity of the
corresponding circuit satisfiability problem
A bi-objective genetic algorithm approach to risk mitigation in project scheduling
A problem of risk mitigation in project scheduling is formulated as a bi-objective optimization problem, where the expected makespan and the expected total cost are both to be minimized. The expected total cost is the sum of four cost components: overhead cost, activity execution cost, cost of reducing risks and penalty cost for tardiness. Risks for activities are predefined. For each risk at an activity, various levels are defined, which correspond to the results of different preventive measures. Only those risks with a probable impact on the duration of the related activity are considered here. Impacts of risks are not only accounted for through the expected makespan but are also translated into cost and thus have an impact on the expected total cost. An MIP model and a heuristic solution approach based on genetic algorithms (GAs) is proposed. The experiments conducted indicate that GAs provide a fast and effective solution approach to the problem. For smaller problems, the results obtained by the GA are very good. For larger problems, there is room for improvement
Approximation Algorithms for the Capacitated Domination Problem
We consider the {\em Capacitated Domination} problem, which models a
service-requirement assignment scenario and is also a generalization of the
well-known {\em Dominating Set} problem. In this problem, given a graph with
three parameters defined on each vertex, namely cost, capacity, and demand, we
want to find an assignment of demands to vertices of least cost such that the
demand of each vertex is satisfied subject to the capacity constraint of each
vertex providing the service. In terms of polynomial time approximations, we
present logarithmic approximation algorithms with respect to different demand
assignment models for this problem on general graphs, which also establishes
the corresponding approximation results to the well-known approximations of the
traditional {\em Dominating Set} problem. Together with our previous work, this
closes the problem of generally approximating the optimal solution. On the
other hand, from the perspective of parameterization, we prove that this
problem is {\it W[1]}-hard when parameterized by a structure of the graph
called treewidth. Based on this hardness result, we present exact
fixed-parameter tractable algorithms when parameterized by treewidth and
maximum capacity of the vertices. This algorithm is further extended to obtain
pseudo-polynomial time approximation schemes for planar graphs
Deterministic Time-Space Tradeoffs for k-SUM
Given a set of numbers, the -SUM problem asks for a subset of numbers
that sums to zero. When the numbers are integers, the time and space complexity
of -SUM is generally studied in the word-RAM model; when the numbers are
reals, the complexity is studied in the real-RAM model, and space is measured
by the number of reals held in memory at any point.
We present a time and space efficient deterministic self-reduction for the
-SUM problem which holds for both models, and has many interesting
consequences. To illustrate:
* -SUM is in deterministic time and space
. In general, any
polylogarithmic-time improvement over quadratic time for -SUM can be
converted into an algorithm with an identical time improvement but low space
complexity as well. * -SUM is in deterministic time and space
, derandomizing an algorithm of Wang.
* A popular conjecture states that 3-SUM requires time on the
word-RAM. We show that the 3-SUM Conjecture is in fact equivalent to the
(seemingly weaker) conjecture that every -space algorithm for
-SUM requires at least time on the word-RAM.
* For , -SUM is in deterministic time and
space
Exact And Representative Algorithms For Multi Objective Optimization
In most real-life problems, the decision alternatives are evaluated with multiple conflicting criteria. The entire set of non-dominated solutions for practical problems is impossible to obtain with reasonable computational effort. Decision maker generally needs only a representative set of solutions from the actual Pareto front. First algorithm we present is for efficiently generating a well dispersed non-dominated solution set representative of the Pareto front which can be used for general multi objective optimization problem. The algorithm first partitions the criteria space into grids to generate reference points and then searches for non-dominated solutions in each grid. This grid-based search utilizes achievement scalarization function and guarantees Pareto optimality. The results of our experimental results demonstrate that the proposed method is very competitive with other algorithms in literature when representativeness quality is considered; and advantageous from the computational efficiency point of view.
Although generating the whole Pareto front does not seem very practical for many real life cases, sometimes it is required for verification purposes or where DM wants to run his decision making structures on the full set of Pareto solutions. For this purpose we present another novel algorithm. This algorithm attempts to adapt the standard branch and bound approach to the multi objective context by proposing to branch on solution points on objective space. This algorithm is proposed for multi objective integer optimization type of problems. Various properties of branch and bound concept has been investigated and explained within the multi objective optimization context such as fathoming, node selection, heuristics, as well as some multi objective optimization specific concepts like filtering, non-domination probability, running in parallel. Potential of this approach for being used both as a full Pareto generation or an approximation approach has been shown with experimental studies
Memetic Multi-Objective Particle Swarm Optimization-Based Energy-Aware Virtual Network Embedding
In cloud infrastructure, accommodating multiple virtual networks on a single
physical network reduces power consumed by physical resources and minimizes
cost of operating cloud data centers. However, mapping multiple virtual network
resources to physical network components, called virtual network embedding
(VNE), is known to be NP-hard. With considering energy efficiency, the problem
becomes more complicated. In this paper, we model energy-aware virtual network
embedding, devise metrics for evaluating performance of energy aware virtual
network-embedding algorithms, and propose an energy aware virtual
network-embedding algorithm based on multi-objective particle swarm
optimization augmented with local search to speed up convergence of the
proposed algorithm and improve solutions quality. Performance of the proposed
algorithm is evaluated and compared with existing algorithms using extensive
simulations, which show that the proposed algorithm improves virtual network
embedding by increasing revenue and decreasing energy consumption.Comment: arXiv admin note: text overlap with arXiv:1504.0684
Linguistic Optimization
Optimality Theory (OT) is a model of language that combines aspects of generative and connectionist linguistics. It is unique in the field in its use of a rank ordering on constraints, which is used to formalize optimization, the choice of the best of a set of potential linguistic forms. We show that phenomena argued to require ranking fall out equally from the form of optimization in OT's predecessor Harmonic Grammar (HG), which uses numerical weights to encode the relative strength of constraints. We further argue that the known problems for HG can be resolved by adopting assumptions about the nature of constraints that have precedents both in OT and elsewhere in computational and generative linguistics. This leads to a formal proof that if the range of each constraint is a bounded number of violations, HG generates a finite number of languages. This is nontrivial, since the set of possible weights for each constraint is nondenumerably infinite. We also briefly review some advantages of HG
- …