A Searching for Strongly Egalitarian and Sex-Equal Stable Matchings Le Hong Trang 1(B ) , Hoang Huu Viet 2 , Tran Van Hoai 1 , and Tran Xuan Hao 2 1 Ho Chi Minh City University of Technology, VNU-HCM, 268 Ly Thuong Kiet, Ho Chi Minh City, Vietnam lhtrang@hcmut.edu.vn 2 Vinh University, 182 Le Duan, Vinh City, Nghe An Province, Vietnam Abstract. The stable marriage problem with ties (SMT) is a variant of the stable marriage problem in which people are permitted to express ties in their preference lists. In this paper, an algorithm based on bidirectional searching is presented for trying to find strongly egalitarian and sex-equal stable matchings. We indicate that the use of two simultaneous searches in the algorithm not only accelerate the finding of solutions but also is appropriate for the strong stability criterion of SMT. The algorithm is implemented and tested for large datasets. Experimental results show that our algorithm is significant. Keywords: Strongly stable · Egalitarian · Sex-equal · Ties · Bidirectional search 1 Introduction An instance I of the classical stable marriage problem (SMP) of size n involves n men and n women. Each man ranks n women to give himself a preference list, and similarly each woman ranks n man to also give herself a preference list. A matching M in I is an one-one correspondence between the men and women of I . For a pair of man and woman (m, w) ∈ M , we denote by M (m) and M (w) the partner of m and w in M , respectively, i.e., w = M (m) and m = M (w). A pair (m, w) is said to be blocking pair for M , if m and w are not partners and m (w, respectively) prefers w (m, respectively) to M (m)(M (w), respectively). A matching that admits no blocking pair is said to be stable, otherwise it is unstable. Let us denote by p m (w)(p w (m), respectively) the position of w (m, respectively) in m’s (w’s, respectively) preference list. It was shown by Gale and Shapley that every instance of SMP admits at least a stable matching [1], and the matching can be found in O(n 2 ). A stable matching found by Gale and Shapley’s algorithm is man- or woman-optimal. c  Springer Nature Switzerland AG 2019 S. Lee et al. (Eds.): IMCOM 2019, AISC 935, pp. 1100–1111, 2019. https://doi.org/10.1007/978-3-030-19063-7_87