Apparatus for use with a heart of a subject, the apparatus comprising: a catheter, transluminally advanceable to the heart; an implant for implantation into the heart comprising a flexible longitudinal member, wherein the flexible longitudinal member is a flexible tubular member, and a linking member that extends from a first linking site of the longitudinal member to a second linking site of the longitudinal member, wherein the implant is adapted to have: a delivery state in which the implant is slidable through at least part of the catheter, the longitudinal member is coaxial with the catheter, and at least a portion of the linking member is disposed alongside the longitudinal member, and an implanted state in which (i) the longitudinal member has one or more portions which traverse the native valve of the heart such that movement of at least one leaflet of the native valve is inhibited, (ii) a first distance between the first linking site and the second linking site, measured along the longitudinal member, is greater than a second distance between the first linking site and the second linking site, measured along the linking member, (iii) the linking member has a mid-portion disposed between the first linking site and the second linking site, and (iv) the mid-portion is not in contact with the longitudinal member; and a plurality of tissue anchors, slidable through the catheter and with respect to the longitudinal member, each tissue anchor of the plurality of tissue anchors configured to anchor a respective portion of the longitudinal member to a respective location of tissue of the heart. a catheter, transluminally advanceable to the heart; an implant for implantation into the heart comprising a flexible longitudinal member, wherein the flexible longitudinal member is a flexible tubular member, and a linking member that extends from a first linking site of the longitudinal member to a second linking site of the longitudinal member, wherein the implant is adapted to have: a delivery state in which the implant is slidable through at least part of the catheter, the longitudinal member is coaxial with the catheter, and at least a portion of the linking member is disposed alongside the longitudinal member, and an implanted state in which (i) the longitudinal member has one or more portions which traverse the native valve of the heart such that movement of at least one leaflet of the native valve is inhibited, (ii) a first distance between the first linking site and the second linking site, measured along the longitudinal member, is greater than a second distance between the first linking site and the second linking site, measured along the linking member, (iii) the linking member has a mid-portion disposed between the first linking site and the second linking site, and (iv) the mid-portion is not in contact with the longitudinal member; and a delivery state in which the implant is slidable through at least part of the catheter, the longitudinal member is coaxial with the catheter, and at least a portion of the linking member is disposed alongside the longitudinal member, and an implanted state in which (i) the longitudinal member has one or more portions which traverse the native valve of the heart such that movement of at least one leaflet of the native valve is inhibited, (ii) a first distance between the first linking site and the second linking site, measured along the longitudinal member, is greater than a second distance between the first linking site and the second linking site, measured along the linking member, (iii) the linking member has a mid-portion disposed between the first linking site and the second linking site, and (iv) the mid-portion is not in contact with the longitudinal member; and a plurality of tissue anchors, slidable through the catheter and with respect to the longitudinal member, each tissue anchor of the plurality of tissue anchors configured to anchor a respective portion of the longitudinal member to a respective location of tissue of the heart.