Hiroki Yanagisawa

Improved approximation results for the stable marriage problem

The stable marriage problem has recently been studied in its general setting, where both ties and incomplete lists are allowed. It is NP-hard to find a stable matching of maximum size, while any stable matching is a maximal matching and thus trivially we can obtain a 2-approximation algorithm. In this article, we give the first nontrivial result for approximation of factor less than two. Our algorithm achieves an approximation ratio of 2/(1 + L−2) for instances in which only men have ties of length at most L. When both men and women are allowed to have ties but the lengths are limited to two, then we show a ratio of 13/7(<1.858). We also improve the lower bound on the approximation ratio to 21/19(>1.1052).

Randomized approximation of the stable marriage problem

While the original stable marriage problem requires all participants to rank all members of the opposite sex in a strict order, two natural variations are to allow for incomplete preference lists and ties in the preferences. Either variation is polynomially solvable, but it has recently been shown to be NP-hard to find a maximum cardinality stable matching when both of the variations are allowed. It is easy to see that the size of any two stable matchings differ by at most a factor of two, and so, an approximation algorithm with a factor two is trivial. In this paper, we give a first nontrivial result for the approximation with factor less than two. Our randomized algorithm achieves a factor of 10/7 for a restricted but still NP-hard case, where ties occur in only mens lists, each man writes at most one tie, and the length of ties is two. Furthermore, we show that these restrictions except for the last one can be removed without increasing the approximation ratio too much.

Dependable virtual machine allocation

The difficulty in allocating virtual machines (VMs) on servers stems from the requirement that sufficient resources (such as CPU capacity and network bandwidth) must be available for each VM in the event of a failure or maintenance work as well as for temporal fluctuations of resource demands, which often exhibit periodic patterns. We propose a mixed integer programming approach that considers the fluctuations of the resource demands for optimal and dependable allocation of VMs. At the heart of the approach are techniques for optimally partitioning the time-horizon into intervals of variable lengths and for reliably estimating the resource demands in each interval. We show that our new approach allocates VMs successfully in a cloud computing environment in a financial company, where the dependability requirement is strict and there are various types of VMs exist.

Improved Approximation of the Stable Marriage Problem

The stable marriage problem has recently been studied in its general setting, where both ties and incomplete lists are allowed. It is NP-hard to find a stable matching of maximum size, while any stable matching is a maximal matching and thus trivially a factor two approximation.

Approximation algorithms for the sex-equal stable marriage problem

The stable marriage problem is a classical matching problem introduced by Gale and Shapley. It is known that for any instance, there exists a solution, and there is a polynomial time algorithm to find one. However, the matching obtained by this algorithm is man-optimal, that is, the matching is favorable for men but unfavorable for women, (or, if we exchange the roles of men and women, the resulting matching is woman-optimal). The sex-equal stable marriage problem, posed by Gusfield and Irving, seeks a stable matching “fair” for both genders. Specifically it seeks a stable matching with the property that the sum of the mens scores is as close as possible to that of the womens. This problem is known to be strongly NP-hard. In this paper, we give a polynomial time algorithm for finding a near optimal solution for the sex-equal stable marriage problem. Furthermore, we consider the problem of optimizing an additional criterion: among stable matchings that are near optimal in terms of the sex-equality, find a minimum egalitarian stable matching. We show that this problem is strongly NP-hard, and give a polynomial time algorithm whose approximation ratio is less than two.

Total Energy Management System for Cloud Computing

Reducing the energy used in Cloud Computing is an important issue a sustainable society. There are many existing approaches for reducing energy use in data centers, but new approaches are needed in case of energy management of Cloud Computing. Cloud Computing involves decentralized data centers, so new flexible way for collecting energy consumption data becomes quite important. Many current approaches focus on reducing energy consumption by air handling equipment, however energy from IT resources also need to be optimized for a total energy management of Cloud Computing. For advanced energy management for Cloud Computing, we developed a Cloud energy management system with sensor management functions, with an optimized VM allocation tool to minimize energy consumption at multiple data centers. Our evaluations showed more than a 30% energy savings for the servers in our experimental environment. Our system can be extended to optimize energy usage from various perspectives, such as for minimizing electricity bills or carbon emissions.

Improved approximation bounds for the Student-Project Allocation problem with preferences over projects

Manlove and O@?Malley (2008) [8] proposed the Student-Project Allocation problem with Preferences over Projects (SPA-P). They proved that the problem of finding a maximum stable matching in SPA-P is APX-hard and gave a polynomial-time 2-approximation algorithm. In this paper, we give an improved upper bound of 1.5 and a lower bound of 21/19 (>1.1052).

A multi-source label-correcting algorithm for the all-pairs shortest paths problem

The All-Pairs Shortest Paths (APSP) problem seeks the shortest path distances between all pairs of vertices, and is one of the most fundamental graph problems. In this paper, a fast algorithm with a small working space for the APSP problem on sparse graphs is presented, which first divides the vertices into sets of vertices with each set having a constant number of vertices and then solves the multi-source shortest paths (MSSP) problem for each set in parallel. For solving the MSSP problems, we give a multi-source label-correcting algorithm, as an extension of a label-correcting algorithm for the single-source shortest path problem. Our algorithm uses fewer operations on the priority queue than an implementation based on Dijkstras algorithm. Our experiments showed that an implementation of our algorithm with SIMD instructions achieves an order of magnitude speedup for real-world geometric graphs compared to an implementation based on Dijkstras algorithm.

An Offline Map Matching via Integer Programming

The map matching problem is, given a spatial road network and a sequence of locations of an object moving on the network, to identify the path in the network that the moving object passed through. In this paper, an integer programming formulation for the offline map matching problem is presented. This is the first approach that gives the optimal solution with respect to a widely used objective function for map matching.

Faster upper bounding of intersection sizes

There is a long history of developing efficient algorithms for set intersection, which is a fundamental operation in information retrieval and databases. In this paper, we describe a new data structure, a Cardinality Filter, to quickly compute an upper bound on the size of a set intersection. Knowing an upper bound of the size can be used to accelerate many applications such as top-k query processing in text mining. Given finite sets A and B, the expected computation time for the upper bound of the size of the intersection |A cap B| is O( (|A| + |B|) w), where w is the machine word length. This is much faster than the current best algorithm for the exact intersection, which runs in O((|A| + |B|) / √w + |A cap B|) expected time. Our performance studies show that our implementations of Cardinality Filters are from 2 to 10 times faster than existing set intersection algorithms, and the time for a top-k query in a text mining application can be reduced by half.