On Box-Perfect Graphs

Let $G=(V,E)$ be a graph and let $A_G$ be the clique-vertex incidence matrix of $G$. It is well known that $G$ is perfect iff the system $A_{_G}\mathbf x\le \mathbf 1$, $\mathbf x\ge\mathbf0$ is totally dual integral (TDI). In 1982, Cameron and Edmonds proposed to call $G$ box-perfect if the system $A_{_G}\mathbf x\le \mathbf 1$, $\mathbf x\ge\mathbf0$ is box-totally dual integral (box-TDI), and posed the problem of characterizing such graphs. In this paper we prove the Cameron-Edmonds conjecture on box-perfectness of parity graphs, and identify several other classes of box-perfect graphs. We also develop a general and powerful method for establishing box-perfectness

Ranking tournaments with no errors I: Structural description

In this series of two papers we examine the classical problem of ranking a set of players on the basis of a set of pairwise comparisons arising from a sports tournament, with the objective of minimizing the total number of upsets, where an upset occurs if a higher ranked player was actually defeated by a lower ranked player. This problem can be rephrased as the so-called minimum feedback arc set problem on tournaments, which arises in a rich variety of applications and has been a subject of extensive research. In this series we study this NP-hard problem using structure-driven and linear programming approaches. Let T=(V,A) be a tournament with a nonnegative integral weight w(e) on each arc e. A subset F of arcs is called a feedback arc set if T\F contains no cycles (directed). A collection C of cycles (with repetition allowed) is called a cycle packing if each arc e is used at most w(e) times by members of C. We call T cycle Mengerian (CM) if, for every nonnegative integral function w defined on A, the minimum total weight of a feedback arc set is equal to the maximum size of a cycle packing. The purpose of these two papers is to show that a tournament is CM iff it contains none of four Möbius ladders as a subgraph; such a tournament is referred to as Möbius-free. In this first paper we present a structural description of all Möbius-free tournaments, which relies heavily on a chain theorem concerning internally 2-strong tournaments

Hybrid Attention-based Encoder-decoder Model for Efficient Language Model Adaptation

Attention-based encoder-decoder (AED) speech recognition model has been widely successful in recent years. However, the joint optimization of acoustic model and language model in end-to-end manner has created challenges for text adaptation. In particular, effectively, quickly and inexpensively adapting text has become a primary concern for deploying AED systems in industry. To address this issue, we propose a novel model, the hybrid attention-based encoder-decoder (HAED) speech recognition model that preserves the modularity of conventional hybrid automatic speech recognition systems. Our HAED model separates the acoustic and language models, allowing for the use of conventional text-based language model adaptation techniques. We demonstrate that the proposed HAED model yields 21\% Word Error Rate (WER) improvements in relative when out-of-domain text data is used for language model adaptation, and with only a minor degradation in WER on a general test set compared with conventional AED model

Ranking tournaments with no errors II: Minimax relation

A tournament T=(V,A) is called cycle Mengerian (CM) if it satisfies the minimax relation on packing and covering cycles, for every nonnegative integral weight function defined on A. The purpose of this series of two papers is to show that a tournament is CM iff it contains none of four Möbius ladders as a subgraph; such a tournament is referred to as Möbius-free. In the first paper we have given a structural description of all Möbius-free tournaments, and have proved that every CM tournament is Möbius-free. In this second paper we establish the converse by using our structural theorems and linear programming approach

A Birandom Job Search Problem with Risk Tolerance

This paper considers a novel class of birandom job search problem, in which the job offers are sampled by the job searcher from a finite job set with equivalent probability and their wages are characterized as independent but maybe not identically nonnegative random variables. The job searcher knows the job offer's wage distribution when he samples the job offer. Since the offered wage is a random variable and the reservation wage is a deterministic number, it is meaningless to make comparison directly. In order to rank the random wage and the reservation wage and provide decision support, a risk tolerance criterion is designed, and the job searcher then accepts or rejects the sampled job offer depending on whether the risk tolerance criterion is met or not. Since the offered wages are random variables and the search process is random, it's impossible to obtain the job searcher's real return; in this case, its expected value can be calculated via birandom theory. Simultaneously, some propositions on the expected return as well as the average search times are also studied which may provide some valuable suggestions to the job searcher. Numerical examples are given to illustrate the decision process of the risk tolerance-based birandom job search problem

Firm-specific knowledge assets and employment arrangements: Evidence from CEO compensation design and CEO dismissal

Ministry of Education, Singapore under its Academic Research Funding Tier