Approximation Algorithms for Survivable Multicommodity Flow Problems with Applications to Network Design

Multicommodity flow (MF) problems have a wide variety of applications in areas such as VLSI circuit design, network design, etc., and are therefore very well studied. The fractional MF problems are polynomial time solvable while integer versions are NP-complete. However, exact algorithms to solve the fractional MF problems have high computational complexity. Therefore approximation algorithms to solve the fractional MF problems have been explored in the literature to reduce their computational complexity. Using these approximation algorithms and the randomized rounding technique, polynomial time approximation algorithms have been explored in the literature. In the design of high-speed networks, such as optical wavelength division multiplexing (WDM) networks, providing survivability carries great significance. Survivability is the ability of the network to recover from failures. It further increases the complexity of network design and presents network designers with more formidable challenges. In this work we formulate the survivable versions of the MF problems. We build approximation algorithms for the survivable multicommodity flow (SMF) problems based on the framework of the approximation algorithms for the MF problems presented in [1] and [2]. We discuss applications of the SMF problems to solve survivable routing in capacitated networks.

Psychological and Support Characteristics of Parents of Child Sexual Abuse Victims: Relationship with Child Functioning and Treatment

Child sexual abuse continues to be a prevalent and complex problem in today’s society as it poses serious and pervasive mental health risks to child victims and their non-offending parents. The main objectives of this study were (a) to elucidate the psychological symptoms and support needs of parents of child sexual abuse victims as they present to group treatment, (b) to examine changes in psychological symptoms and support needs and their relationship with child functioning over the course of a parallel group treatment, and (c) to examine the impact of these factors on completion of group treatment. Participants included 104 sexually abused youth and their non-offending parent presenting to Project SAFE Group Intervention, a 12-session cognitive-behavioral group treatment for sexually abused children and their non-offending parents. This project had a unique advantage of utilizing a variety of demographic, parent-, and child-report measures, allowing for a more comprehensive examination of change in symptomatology and needs over the course of treatment. Several significant findings were noted, including the identification of four clusters of youth at pre-treatment, which were maintained at post-treatment; elevations on the CTQ Sexual Abuse scale; parents of youth sexually abused by a non-family member had significantly higher PSI-Restriction of Role subscale scores; parental expectations of a negative impact on their child were worse for older children; several parent characteristics predicted client treatment retention (e.g., older parents, lower SCL-90-R GSI scores); and an early age of onset of abuse also increased treatment retention. Future directions, recommendations, and limitations were discussed.