arXiv subjects

Toshiya Itoh

Publications and source records attributed to Toshiya Itoh.

25 records · Page 2Linked to original sources

arXiv2016

Optimal Online Algorithms for the Multi-Objective Time Series Search Problem

Tiedemann, et al. [Proc. of WALCOM, LNCS 8973, 2015, pp.210-221] defined multi-objective online problems (as an online version of multi-objective optimization problems) and the competitive analysis for multi-objective online problems and showed that (1) with respect to the worst component competitive analysis, the online algorithm RPP-HIGH is best possible for the multi-objective time series search~problem; (2) with respect to the arithmetic mean component competitive analysis, the online algorithm RPP-MULT is best possible for the bi-objective time series search problem; (3) with respect to the geometric mean component competitive analysis, the online algorithm RPP-MULT is best possible for the bi-objective time series search problem. In this paper, we first point out that the definitions and frameworks of the competitive analysis due to Tiedemann, et al. do not necessarily capture the efficiency of online algorithms for multi-objective online problems and provide modified definitions of the competitive analysis for multi-objective online problems. Then under the modified framework, we present a simple online algorithm Balanced Price Policy BPP_{k} for the multi-objective (k-objective) time series search problem, and show that the algorithm BPP_{k} is best possible with respect to any measure of the competitive analysis (defined by a monotone continuous function f). Under the modified framework, we derive exact values of the competitive ratio for the multi-objective time series search problem with respect to the worst component competitive analysis, the arithmetic mean component competitive analysis, and the geometric mean component competitive analysis.

cs.DS↗

arXiv2013

Buffer Management of Multi-Queue QoS Switches with Class Segregation

In this paper, we focus on buffer management of multi-queue QoS switches in which packets of different values are segregated in different queues. Our model consists of $m$ queues and $m$ packet values $0 < v_{1} < v_{2} < ... < v_{m}$. Recently, Al-Bawani and Souza [IPL 113(4), pp.145-150, 2013] presented an online algorithm GREEDY for buffer management of multi-queue QoS switches with class segregation and showed thatif $m$ queues have the same size, then the competitive ratio of GREEDY is $1+r$, where $r=\max_{1 \leq i \leq m-1} v_{i}/v_{i+1}$. In this paper, we precisely analyze the behavior of GREEDY and show that it is $(1+r)$-competitive for the case that $m$ queues do not necessarily have the same size.

cs.DS↗

arXiv2011

Greedy Algorithms for Multi-Queue Buffer Management with Class Segregation

In this paper, we focus on a multi-queue buffer management in which packets of different values are segregated in different queues. Our model consists of m packets values and m queues. Recently, Al-Bawani and Souza (arXiv:1103.6049v2 [cs.DS] 30 Mar 2011) presented an online multi-queue buffer management algorithm Greedy and showed that it is 2-competitive for the general m-valued case, i.e., m packet values are 0 < v_{1} < v_{2} < ... < v_{m}, and (1+v_{1}/v_{2})-competitive for the two-valued case, i.e., two packet values are 0 < v_{1} < v_{2}. For the general m-valued case, let c_i = (v_{i} + \sum_{j=1}^{i-1} 2^{j-1} v_{i-j})/(v_{i+1} + \sum_{j=1}^{i-1}2^{j-1}v_{i-j}) for 1 \leq i \leq m-1, and let c_{m}^{*} = \max_{i} c_{i}. In this paper, we precisely analyze the competitive ratio of Greedy for the general m-valued case, and show that the algorithm Greedy is (1+c_{m}^{*})-competitive.

cs.DM↗

arXiv2008

New Constructions for Query-Efficient Locally Decodable Codes of Subexponential Length

A $(k,δ,ε)$-locally decodable code $C: F_{q}^{n} \to F_{q}^{N}$ is an error-correcting code that encodes each message $\vec{x}=(x_{1},x_{2},...,x_{n}) \in F_{q}^{n}$ to $C(\vec{x}) \in F_{q}^{N}$ and has the following property: For any $\vec{y} \in {\bf F}_{q}^{N}$ such that $d(\vec{y},C(\vec{x})) \leq δN$ and each $1 \leq i \leq n$, the symbol $x_{i}$ of $\vec{x}$ can be recovered with probability at least $1-ε$ by a randomized decoding algorithm looking only at $k$ coordinates of $\vec{y}$. The efficiency of a $(k,δ,ε)$-locally decodable code $C: F_{q}^{n} \to F_{q}^{N}$ is measured by the code length $N$ and the number $k$ of queries. For any $k$-query locally decodable code $C: F_{q}^{n} \to F_{q}^{N}$, the code length $N$ is conjectured to be exponential of $n$, however, this was disproved. Yekhanin [In Proc. of STOC, 2007] showed that there exists a 3-query locally decodable code $C: F_{2}^{n} \to F_{2}^{N}$ such that $N=\exp(n^{(1/\log \log n)})$ assuming that the number of Mersenne primes is infinite. For a 3-query locally decodable code $C: F_{q}^{n} \to F_{q}^{N}$, Efremenko [ECCC Report No.69, 2008] reduced the code length further to $N=\exp(n^{O((\log \log n/ \log n)^{1/2})})$, and also showed that for any integer $r>1$, there exists a $k$-query locally decodable code $C: F_{q}^{n} \to F_{q}^{N}$ such that $k \leq 2^{r}$ and $N=\exp(n^{O((\log \log n/ \log n)^{1-1/r})})$. In this paper, we present a query-efficient locally decodable code and show that for any integer $r>1$, there exists a $k$-query locally decodable code $C: F_{q}^{n} \to F_{q}^{N}$ such that $k \leq 3 \cdot 2^{r-2}$ and $N=\exp(n^{O((\log \log n/ \log n)^{1-1/r})})$.

cs.CC↗

arXiv2008

Approximation Algorithms for the Highway Problem under the Coupon Model

When a store sells items to customers, the store wishes to determine the prices of the items to maximize its profit. Intuitively, if the store sells the items with low (resp. high) prices, the customers buy more (resp. less) items, which provides less profit to the store. So it would be hard for the store to decide the prices of items. Assume that the store has a set V of n items and there is a set E of m customers who wish to buy those items, and also assume that each item i \in V has the production cost d_i and each customer e_j \in E has the valuation v_j on the bundle e_j \subseteq V of items. When the store sells an item i \in V at the price r_i, the profit for the item i is p_i=r_i-d_i. The goal of the store is to decide the price of each item to maximize its total profit. In most of the previous works, the item pricing problem was considered under the assumption that p_i \geq 0 for each i \in V, however, Balcan, et al. [In Proc. of WINE, LNCS 4858, 2007] introduced the notion of loss-leader, and showed that the seller can get more total profit in the case that p_i < 0 is allowed than in the case that p_i < 0 is not allowed. In this paper, we consider the line and the cycle highway problem, and show approximation algorithms for the line and/or cycle highway problem for which the smallest valuation is s and the largest valuation is \ell or all valuations are identical.

cs.DS↗

arXiv2007

Weighted Random Popular Matchings

For a set A of n applicants and a set I of m items, we consider a problem of computing a matching of applicants to items, i.e., a function M mapping A to I; here we assume that each applicant $x \in A$ provides a preference list on items in I. We say that an applicant $x \in A$ prefers an item p than an item q if p is located at a higher position than q in its preference list, and we say that x prefers a matching M over a matching M' if x prefers M(x) over M'(x). For a given matching problem A, I, and preference lists, we say that M is more popular than M' if the number of applicants preferring M over M' is larger than that of applicants preferring M' over M, and M is called a popular matching if there is no other matching that is more popular than M. Here we consider the situation that A is partitioned into $A_{1},A_{2},...,A_{k}$, and that each $A_{i}$ is assigned a weight $w_{i}>0$ such that w_{1}>w_{2}>...>w_{k}>0$. For such a matching problem, we say that M is more popular than M' if the total weight of applicants preferring M over M' is larger than that of applicants preferring M' over M, and we call M an k-weighted popular matching if there is no other matching that is more popular than M. In this paper, we analyze the 2-weighted matching problem, and we show that (lower bound) if $m/n^{4/3}=o(1)$, then a random instance of the 2-weighted matching problem with $w_{1} \geq 2w_{2}$ has a 2-weighted popular matching with probability o(1); and (upper bound) if $n^{4/3}/m = o(1)$, then a random instance of the 2-weighted matching problem with $w_{1} \geq 2w_{2}$ has a 2-weighted popular matching with probability 1-o(1).

cs.DM↗

arXiv2006

Primal-dual distance bounds of linear codes with application to cryptography

Let $N(d,d^\perp)$ denote the minimum length $n$ of a linear code $C$ with $d$ and $d^{\bot}$, where $d$ is the minimum Hamming distance of $C$ and $d^{\bot}$ is the minimum Hamming distance of $C^{\bot}$. In this paper, we show a lower bound and an upper bound on $N(d,d^\perp)$. Further, for small values of $d$ and $d^\perp$, we determine $N(d,d^\perp)$ and give a generator matrix of the optimum linear code. This problem is directly related to the design method of cryptographic Boolean functions suggested by Kurosawa et al.

cs.IT↗